A294846 Expansion of Product_{k>=1} 1/(1 + x^k)^(k*(k+1)/2).

1, -1, -2, -4, 0, 3, 17, 24, 40, 9, -24, -149, -250, -435, -395, -281, 514, 1528, 3542, 5127, 6920, 5416, 1368, -11136, -28533, -57051, -82846, -107315, -95655, -43646, 107826, 345877, 727771, 1150968, 1601729, 1766547, 1495154, 183944, -2339567, -6770991, -12701854

Offset

0,3

Comments

Convolution inverse of A028377.

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = n*(n+1)/2, g(n) = -1. - Seiichi Manyama, Nov 14 2017

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Formula

G.f.: Product_{k>=1} 1/(1 + x^k)^A000217(k).

a(0) = 1 and a(n) = (1/(2*n)) * Sum_{k=1..n} b(k)*a(n-k) where b(n) = Sum_{d|n} d^2*(d+1)*(-1)^(n/d). - Seiichi Manyama, Nov 14 2017

Mathematica

nmax = 40; CoefficientList[Series[Product[1/(1 + x^k)^(k (k + 1)/2), {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, -Sum[Sum[(-1)^(k/d + 1) d^2 (d + 1)/2, {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 40}]

Crossrefs

Cf. A000217, A000294, A028377, A255528, A284896, A292386.

Sequence in context: A330473 A198543 A367468 * A011994 A258773 A054003

Adjacent sequences: A294843 A294844 A294845 * A294847 A294848 A294849

Keyword

sign

Author

Ilya Gutkovskiy, Nov 09 2017

Status

approved