A354574 E.g.f. A(x) satisfies A(x) = 1 + x * A(1 - exp(-x)).

1, 1, 2, 3, -8, -65, 366, 4284, -71392, -377919, 28218760, -249587877, -14356069056, 587285561746, 153563287892, -954498079774950, 39921820513516256, 533333406684245239, -158979463609003391970, 8008135971419079188618, 190727236066813163686860

Offset

0,3

Links

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

Formula

a(0) = 1; a(n) = n * Sum_{k=0..n-1} (-1)^(n-k-1) * Stirling2(n-1,k) * a(k).

a(n) = n * A353177(n-1) for n>0.

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*sum(j=0, i-1, (-1)^(i-j-1)*stirling(i-1, j, 2)*v[j+1])); v;

Crossrefs

Cf. A048801, A353177, A354729, A354730.

Sequence in context: A351658 A003096 A333077 * A042815 A191353 A319218

Adjacent sequences: A354571 A354572 A354573 * A354575 A354576 A354577

Keyword

sign

Author

Seiichi Manyama, Jun 04 2022

Status

approved