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A158098
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Euler transform of triangular powers of 2: [2,2^3,2^6,...,2^(n(n+1)/2),...].
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2
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1, 2, 11, 84, 1217, 35630, 2177587, 273084984, 69282922119, 35324981861270, 36099947418619965, 73859427092428467556, 302379428224074427461199, 2476485356209583877951854650, 40569774298249879934939059013965, 1329309152683489963994724570066550944
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OFFSET
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0,2
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..81
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FORMULA
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G.f.: A(x) = 1/Product_{n>=1} (1 - x^n)^(2^(n(n+1)/2)).
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*add(
d*2^(d*(d+1)/2), d=numtheory[divisors](j)), j=1..n)/n)
end:
seq(a(n), n=0..20); # Alois P. Heinz, Jul 28 2017
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MATHEMATICA
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a[n_] := a[n] = If[n==0, 1, Sum[a[n-j] Sum[d 2^(d(d+1)/2), {d, Divisors[j]}], {j, 1, n}]/n];
a /@ Range[0, 20] (* Jean-François Alcover, Nov 20 2020, after Alois P. Heinz *)
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PROG
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(PARI) a(n)=polcoeff(1/prod(k=1, n, (1-x^k+x*O(x^n))^(2^(k*(k+1)/2))), n)
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CROSSREFS
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Cf. A006125, A158099.
Sequence in context: A191805 A279202 A086406 * A104185 A074604 A135404
Adjacent sequences: A158095 A158096 A158097 * A158099 A158100 A158101
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Mar 20 2009
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STATUS
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approved
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