A367922 Expansion of e.g.f. 1/(1 - x + 2*log(1 - x)).

1, 3, 20, 202, 2724, 45928, 929288, 21936864, 591822912, 17962293408, 605744322048, 22470338716032, 909323575700352, 39864781715364864, 1882110048700328448, 95205899353680970752, 5137022051563160623104, 294501790029090740576256

Offset: 0

Author

Seiichi Manyama, Dec 05 2023

Keywords

• nonn

Crossrefs

Cf. A052820, A367923.

Cf. A367845.

Programs

PARI

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*v[i]+2*sum(j=1, i, (j-1)!*binomial(i, j)*v[i-j+1])); v;

Formula

a(0) = 1; a(n) = n * a(n-1) + 2 * Sum_{k=1..n} (k-1)! * binomial(n,k) * a(n-k).