A307260 Expansion of (1/(1 + x)) * Product_{k>=1} (1 + k*x^k/(1 + x)^k).

1, 0, 1, 1, -4, 14, -35, 77, -161, 356, -873, 2267, -5787, 13850, -30361, 59934, -103754, 147968, -139049, -58998, 730972, -2430881, 6333238, -15548722, 39845197, -110775861, 325257904, -960503811, 2756222486, -7568564555, 19815541729, -49548068461, 118752506024

Offset

0,5

Comments

Inverse binomial transform of A022629.

Links

Table of n, a(n) for n=0..32.

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n,k)*A022629(k).

Maple

a:=series((1/(1+x))*mul(1+k*x^k/(1+x)^k, k=1..100), x=0, 33): seq(coeff(a, x, n), n=0..32); # Paolo P. Lava, Apr 03 2019

Mathematica

nmax = 32; CoefficientList[Series[1/(1 + x) Product[(1 + k x^k/(1 + x)^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A022629, A293467, A294503, A307258, A307259.

Sequence in context: A362342 A197275 A011852 * A288678 A295180 A305906

Adjacent sequences: A307257 A307258 A307259 * A307261 A307262 A307263

Keyword

sign

Author

Ilya Gutkovskiy, Apr 01 2019

Status

approved