A379878 E.g.f. A(x) satisfies A(x) = exp(-x) + x*A(x)^3.

1, 0, 1, 8, 97, 1544, 30673, 732752, 20486401, 656713520, 23755416481, 957430990328, 42552022022497, 2067669370359800, 109058922249721585, 6205740584180119424, 378947624701223801089, 24718152376534891564256, 1715322065909959400535361, 126186162087426817989206888

Offset

0,4

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = -n! * Sum_{k=0..n} (-2*k-1)^(n-k-1) * binomial(3*k,k)/(n-k)!.

a(n) ~ (-1)^n * sqrt(-LambertW(-8/27) - 1) * 2^n * n^(n-1) / (3 * exp(n) * LambertW(-8/27)^(n + 1/2)). - Vaclav Kotesovec, Jan 23 2025

Mathematica

Table[-n! * Sum[(-2*k-1)^(n-k-1) * Binomial[3*k, k] / (n-k)!, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jan 23 2025 *)

Prog

(PARI) a(n) = -n!*sum(k=0, n, (-2*k-1)^(n-k-1)*binomial(3*k, k)/(n-k)!);

Crossrefs

Cf. A379871, A379876, A379877.

Cf. A000166, A379879.

Sequence in context: A262777 A367493 A365845 * A292747 A083182 A302277

Adjacent sequences: A379875 A379876 A379877 * A379879 A379880 A379882

Keyword

nonn,changed

Author

Seiichi Manyama, Jan 05 2025

Status

approved