A354611 Expansion of e.g.f. 1/(2 - (1 - x)^x).

1, 0, -2, -3, 28, 150, -714, -10920, 13392, 1129464, 3694680, -150143400, -1515256104, 22631946480, 525582087408, -2756199995640, -192774443051520, -525316900812480, 75951597634314048, 926307802605928320, -30597152030347651200, -833744424171043728000

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A007114(k) * binomial(n,k) * a(n-k).

Prog

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

Crossrefs

Cf. A007114, A354610.

Sequence in context: A052848 A357267 A074233 * A356906 A371115 A206592

Adjacent sequences: A354608 A354609 A354610 * A354612 A354613 A354614

Keyword

sign

Author

Seiichi Manyama, Jul 08 2022

Status

approved