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A119304
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Triangle read by rows: T(n,k) = binomial(4n-k,n-k), 0 <= k <= n.
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2
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1, 4, 1, 28, 7, 1, 220, 55, 10, 1, 1820, 455, 91, 13, 1, 15504, 3876, 816, 136, 16, 1, 134596, 33649, 7315, 1330, 190, 19, 1, 1184040, 296010, 65780, 12650, 2024, 253, 22, 1, 10518300, 2629575, 593775, 118755, 20475, 2925, 325, 25, 1, 94143280, 23535820
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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Indranil Ghosh, Rows 0..125, flattened
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FORMULA
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Riordan array (1/(1-4f(x)),f(x)) where f(x)(1-f(x))^3 = x.
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EXAMPLE
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Triangle begins
1;
4, 1;
28, 7, 1;
220, 55, 10, 1;
1820, 455, 91, 13, 1;
15504, 3876, 816, 136, 16, 1;
134596, 33649, 7315, 1330, 190, 19, 1;
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MATHEMATICA
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Flatten[Table[Binomial[4n-k, n-k], {n, 0, 9}, {k, 0, n}]] (* Indranil Ghosh, Feb 26 2017 *)
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PROG
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(PARI) tabl(nn) = {for (n=0, nn, for (k=0, n, print1(binomial(4*n-k, n-k), ", "); ); print(); ); } \\ Indranil Ghosh, Feb 26 2017
(Python)
from sympy import binomial
i=0
for n in range(12):
for k in range(n+1):
print(str(i)+" "+str(binomial(4*n-k, n-k)))
i+=1 # Indranil Ghosh, Feb 26 2017
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CROSSREFS
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Rows sums are A052203. First column is A005810. Inverse of A119305.
Sequence in context: A134150 A134151 A264773 * A114150 A134149 A035469
Adjacent sequences: A119301 A119302 A119303 * A119305 A119306 A119307
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry, May 13 2006
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STATUS
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approved
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