A355123 E.g.f. A(x) satisfies A(x) = 1 + (1 - exp(-x)) * A(2 * (1 - exp(-x))).

1, 1, 3, 25, 611, 41721, 7326115, 3120454233, 3105527125475, 7041597540281017, 35733375744777784867, 400526056950063657595929, 9816824637930442994222501475, 521959475771315485798501882623609, 59814953381855591853355367174623538851

Offset

0,3

Links

Table of n, a(n) for n=0..14.

Formula

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

a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(n-k) * k * 2^(k-1) * Stirling2(n,k) * a(k-1).

Prog

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

Crossrefs

Cf. A353177, A355093.

Sequence in context: A213599 A179473 A248417 * A306795 A131310 A362657

Adjacent sequences: A355120 A355121 A355122 * A355124 A355125 A355126

Keyword

nonn

Author

Seiichi Manyama, Jun 20 2022

Status

approved