A357193 a(n) = n! * Sum_{k=0..floor(n/2)} k^(2*n)/k!.

1, 0, 2, 6, 3096, 61560, 65248200, 4058986680, 7506140268480, 1062517243193280, 3052268000677879200, 822543740977513816800, 3395913346775619237617280, 1553795963458841732838848640, 8727392877498334693600263757440

Offset

0,3

Links

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

Formula

E.g.f.: Sum_{k>=0} (k^2 * x)^(2 * k) / (k! * (1 - k^2 * x)).

Prog

(PARI) a(n) = n!*sum(k=0, n\2, k^(2*n)/k!);
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k^2*x)^(2*k)/(k!*(1-k^2*x)))))

Crossrefs

Cf. A256016, A357194.

Cf. A352983, A357191.

Sequence in context: A071093 A114045 A116899 * A355556 A162146 A231545

Adjacent sequences: A357190 A357191 A357192 * A357194 A357195 A357196

Keyword

nonn

Author

Seiichi Manyama, Sep 17 2022

Status

approved