A356630 a(n) = n! * Sum_{k=0..floor(n/4)} (n - 4*k)^k/(n - 4*k)!.

1, 1, 1, 1, 1, 121, 721, 2521, 6721, 378001, 7287841, 59930641, 319429441, 7524471241, 353072319601, 5897248517161, 55827317669761, 726274560953761, 53139878190826561, 1650487849152976801, 25981849479032542081, 317292238756098973081

Offset

0,6

Links

Table of n, a(n) for n=0..21.

Formula

E.g.f.: Sum_{k>=0} x^k / (k! * (1 - k*x^4)).

Mathematica

a[n_] := n! * Sum[(n - 4*k)^k/(n - 4*k)!, {k, 0, Floor[n/4]}]; a[0] = 1; Array[a, 22, 0] (* Amiram Eldar, Aug 19 2022 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\4, (n-4*k)^k/(n-4*k)!);
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(k!*(1-k*x^4)))))

Crossrefs

Cf. A354436, A356628, A356629.

Cf. A354554, A356634.

Sequence in context: A367720 A293566 A293507 * A306452 A238250 A361658

Adjacent sequences: A356627 A356628 A356629 * A356631 A356632 A356633

Keyword

nonn

Author

Seiichi Manyama, Aug 18 2022

Status

approved