A355104 E.g.f. A(x) satisfies A(x) = 1 + 2 * x * A(log(1+x)).

1, 2, 8, 36, 128, -120, -5904, 8792, 1015808, -7346016, -403678560, 9772765552, 226781102016, -17673167204576, 72041280334240, 38308664521315920, -1705420687695700992, -64315848872486436736, 11313330167773175073408, -326450445457848188386944

Offset: 0

Author

Seiichi Manyama, Jun 19 2022

Keywords

• sign

Crossrefs

Cf. A354729, A355105.

Cf. A355096.

Programs

PARI

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

Formula

a(0) = 1; a(n) = 2 * n * Sum_{k=0..n-1} Stirling1(n-1,k) * a(k).

a(n) = 2 * n * A355096(n-1) for n>0.