A355720 Expansion of e.g.f. exp( x/(2 - exp(x)) ).

1, 1, 3, 16, 113, 986, 10237, 123096, 1680737, 25668766, 433329461, 8009178596, 160802065393, 3483842906610, 80992799730221, 2010720004254856, 53081510001375041, 1484613248976841958, 43846812123456425221, 1363477059263944382604

Offset

0,3

Links

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

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A052882(k) * binomial(n-1,k-1) * a(n-k).

a(n) ~ n^(n - 1/4) * exp(sqrt(2*n) - 1/4 - n) / (sqrt(2) * log(2)^n). - Vaclav Kotesovec, Jul 15 2022

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x/(2-exp(x)))))
(PARI) a000670(n) = sum(k=0, n, k!*stirling(n, k, 2));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, j*a000670(j-1)*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A000248, A355718, A355719.

Cf. A000670, A052882, A075729.

Sequence in context: A379193 A332024 A124537 * A305133 A368510 A074523

Adjacent sequences: A355717 A355718 A355719 * A355721 A355722 A355723

Keyword

nonn

Author

Seiichi Manyama, Jul 15 2022

Status

approved