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
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Nov 09 2017
STATUS
approved