A357146 a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^(2*k)/(n - 2*k)!.

1, 1, 1, 7, 49, 301, 6241, 74131, 1722337, 46346329, 1090339201, 48905462431, 1584330498961, 81705172522117, 4191355357015009, 223743062044497451, 16563314120270608321, 1027165911865738200241, 91346158358120706564097, 7395168869747626389974839

Offset

0,4

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A354436, A357147.

Cf. A353016, A356628.

Sequence in context: A113235 A294261 A294293 * A133046 A200783 A267230

Adjacent sequences: A357143 A357144 A357145 * A357147 A357148 A357149

Keyword

nonn

Author

Seiichi Manyama, Sep 15 2022

Status

approved