A354613 Expansion of e.g.f. 1/(2 - (1 + x)^x).

1, 0, 2, -3, 44, -210, 2694, -23520, 330672, -4168584, 67622040, -1095648840, 20621674776, -403514963280, 8734659594192, -199049377658040, 4894304369356800, -126907901533425600, 3501394314254828352, -101643840316833194880, 3112491474764866339200

Offset

0,3

Links

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

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A007113(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, stirling(j-k, k, 1)/(j-k)!)*binomial(i, j)*v[i-j+1])); v;

Crossrefs

Cf. A007113, A354612.

Sequence in context: A255969 A329945 A239850 * A375687 A355842 A100443

Adjacent sequences: A354610 A354611 A354612 * A354614 A354615 A354616

Keyword

sign

Author

Seiichi Manyama, Jul 08 2022

Status

approved