A354147 Expansion of e.g.f. 1/(1 - 4 * log(1+x)).

1, 4, 28, 296, 4168, 73376, 1550048, 38202048, 1076017344, 34096092672, 1200459182592, 46492497859584, 1964295942558720, 89906908894150656, 4431634108980264960, 234044235939806232576, 13184410813249253031936, 789137065405617987354624

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(0) = 1; a(n) = 4 * Sum_{k=1..n} (-1)^(k-1) * (k-1)! * binomial(n,k) * a(n-k).

a(n) = Sum_{k=0..n} 4^k * k! * Stirling1(n, k).

a(n) ~ n! * exp(1/4) / (4 * (exp(1/4)-1)^(n+1)). - Vaclav Kotesovec, Jun 04 2022

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-4*log(1+x))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=4*sum(j=1, i, (-1)^(j-1)*(j-1)!*binomial(i, j)*v[i-j+1])); v;
(PARI) a(n) = sum(k=0, n, 4^k*k!*stirling(n, k, 1));

Crossrefs

Column k=4 of A320080.

Cf. A094417, A354240, A354264.

Sequence in context: A112938 A307083 A343709 * A362475 A372738 A274043

Adjacent sequences: A354144 A354145 A354146 * A354148 A354149 A354150

Keyword

nonn

Author

Seiichi Manyama, May 21 2022

Status

approved