A329260 Expansion of e.g.f. -log(1 - Sum_{k>=0} x^(2^k) / (2^k)!).

0, 1, 2, 5, 22, 119, 825, 6810, 65766, 725139, 8997795, 124039530, 1881019965, 31117851270, 557686108980, 10763514011250, 222577767068086, 4909509776289707, 115059754193953599, 2855172351859669458, 74786346248906702415, 2062000166613319934190

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(0) = 0; a(n) = A209229(n) + (1/n) * Sum_{k=1..n-1} binomial(n,k) * A209229(n-k) * k * a(k).

Mathematica

nmax = 21; CoefficientList[Series[-Log[1 - Sum[x^(2^k)/(2^k)!, {k, 0, Floor[Log[2, nmax]] + 1}]], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Boole[IntegerQ[Log[2, n]]] + Sum[Binomial[n, k] Boole[IntegerQ[Log[2, n - k]]] k a[k], {k, 1, n - 1}]/n; a[0] = 0; Table[a[n], {n, 0, 21}]

Crossrefs

Cf. A000629, A115625, A209229.

Sequence in context: A015557 A066305 A020093 * A111542 A342432 A246542

Adjacent sequences: A329257 A329258 A329259 * A329261 A329262 A329263

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 09 2019

Status

approved