A354327 Expansion of e.g.f. 1/(1 + x/4 * log(1 - 2 * x)).

1, 0, 1, 3, 22, 180, 1902, 23730, 344872, 5706288, 105960600, 2181449160, 49311653616, 1214109056160, 32339248301808, 926527371653520, 28410493609687680, 928335829570087680, 32201658919855225728, 1181755749910942408320, 45744743939940787150080

Offset

0,4

Links

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

Formula

a(0) = 1; a(n) = n! * Sum_{k=2..n} 2^(k-3)/(k-1) * a(n-k)/(n-k)!.

a(n) = n! * Sum_{k=0..floor(n/2)} 2^(n-3*k) * k! * |Stirling1(n-k,k)|/(n-k)!.

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x/4*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-3)/(j-1)*v[i-j+1]/(i-j)!)); v;
(PARI) a(n) = n!*sum(k=0, n\2, 2^(n-3*k)*k!*abs(stirling(n-k, k, 1))/(n-k)!);

Crossrefs

Cf. A052830, A187735, A354325, A354328.

Sequence in context: A362691 A138899 A147855 * A278333 A132595 A065204

Adjacent sequences: A354324 A354325 A354326 * A354328 A354329 A354330

Keyword

nonn

Author

Seiichi Manyama, May 24 2022

Status

approved