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0, 1, 5, 14, 31, 60, 106, 176, 279, 426, 631, 912, 1291, 1795, 2457, 3317, 4424, 5837, 7626, 9875, 12684, 16171, 20476, 25764, 32228, 40094, 49626, 61131, 74966, 91545, 111346, 134921, 162906, 196031, 235134, 281175, 335251, 398615, 472695, 559115, 659721, 776608
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..41.
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FORMULA
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a(n) = Sum_{k=0..n} A000009(k) * (n-k)^2.
G.f.: x*(1+x)/(1-x)^3 * Product_{k>=1} (1 + x^k).
a(n) ~ 4 * 3^(5/4) * n^(3/4) * exp(sqrt(n/3)*Pi) / Pi^3.
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MAPLE
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b:= proc(n) option remember; `if`(n=0, 1, add(b(n-j)*add(
`if`(d::odd, d, 0), d=numtheory[divisors](j)), j=1..n)/n)
end:
a:= n-> add(b(n-j)*j^2, j=0..n):
seq(a(n), n=0..42); # Alois P. Heinz, Feb 09 2023
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MATHEMATICA
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Table[Sum[PartitionsQ[k]*(n-k)^2, {k, 0, n}], {n, 0, 60}]
CoefficientList[Series[x*(1+x)*QPochhammer[-1, x] / (2*(1-x)^3), {x, 0, 60}], x]
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CROSSREFS
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Cf. A000009, A000290, A095944, A360486.
Sequence in context: A299903 A299276 A267167 * A023652 A283523 A101648
Adjacent sequences: A360484 A360485 A360486 * A360488 A360489 A360490
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KEYWORD
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nonn
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AUTHOR
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Vaclav Kotesovec, Feb 09 2023
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STATUS
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approved
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