A354315 Expansion of e.g.f. 1/(1 + x/2 * log(1 - 2 * x)).

1, 0, 2, 6, 56, 480, 5664, 75600, 1182208, 20829312, 410768640, 8943010560, 213187497984, 5520777799680, 154333888579584, 4631752470159360, 148523272512307200, 5067610703150284800, 183308248516478828544, 7006773595450681589760, 282194468488468121518080

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

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

a(n) = n! * Sum_{k=0..floor(n/2)} 2^(n-2*k) * k! * |Stirling1(n-k,k)|/(n-k)!.

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x/2*log(1-2*x))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i!*sum(j=2, i, 2^(j-2)/(j-1)*v[i-j+1]/(i-j)!)); v;
(PARI) a(n) = n!*sum(k=0, n\2, 2^(n-2*k)*k!*abs(stirling(n-k, k, 1))/(n-k)!);

Crossrefs

Cf. A052830, A354316.

Cf. A354309, A354327.

Sequence in context: A181509 A213026 A074023 * A000146 A318001 A211933

Adjacent sequences: A354312 A354313 A354314 * A354316 A354317 A354318

Keyword

nonn

Author

Seiichi Manyama, May 23 2022

Status

approved