A353546 Expansion of e.g.f. -log(1-2*x) * exp(x)/2.

0, 1, 4, 17, 96, 729, 7060, 83033, 1146656, 18164625, 324488068, 6450956929, 141233271872, 3376008830505, 87480173354964, 2442396780039817, 73089894980585408, 2333809837398044321, 79198287879591647364, 2846319497398561356913

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = n! * Sum_{k=0..n-1} 2^(n-1-k) / ((n-k) * k!).

a(0) = 0, a(1) = 1, a(n) = (2 * n - 1) * a(n-1) - 2 * (n-1) * a(n-2) + 1.

a(n) ~ (n-1)! * exp(1/2) * 2^(n-1). - Vaclav Kotesovec, Jun 08 2022

Prog

(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-log(1-2*x)*exp(x)/2)))
(PARI) a(n) = n!*sum(k=0, n-1, 2^(n-1-k)/((n-k)*k!));
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=0; v[2]=1; for(i=2, n, v[i+1]=(2*i-1)*v[i]-2*(i-1)*v[i-1]+1); v;

Crossrefs

Cf. A002104, A353547, A353548, A353549.

Cf. A346394.

Essentially partial sums of A010844.

Sequence in context: A123750 A278644 A249078 * A024052 A128321 A290352

Adjacent sequences: A353543 A353544 A353545 * A353547 A353548 A353549

Keyword

nonn

Author

Seiichi Manyama, May 27 2022

Status

approved