A371066 E.g.f. satisfies A(x) = 1 + x^3/6*exp(x*A(x)).

1, 0, 0, 1, 4, 10, 20, 175, 2296, 20244, 134520, 1016565, 13527580, 209970046, 2785823404, 33569936855, 467250784560, 8358652382760, 159820481883696, 2888819281378089, 51781860691882740, 1031576680142770930, 23237341150372569220, 543570375735294712651

Offset

0,5

Links

Table of n, a(n) for n=0..23.

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} k^(n-3*k) * binomial(n-3*k+1,k)/( 6^k*(n-3*k+1)*(n-3*k)! ).

Mathematica

nmax = 20; CoefficientList[Series[1 - ProductLog[-E^x*x^4/6]/x, {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Mar 10 2024 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\3, k^(n-3*k)*binomial(n-3*k+1, k)/(6^k*(n-3*k+1)*(n-3*k)!));

Crossrefs

Cf. A161631, A371063.

Cf. A371044.

Sequence in context: A339784 A277970 A229884 * A038422 A009870 A300742

Adjacent sequences: A371063 A371064 A371065 * A371067 A371068 A371069

Keyword

nonn

Author

Seiichi Manyama, Mar 09 2024

Status

approved