A373683 - OEIS

A373683

Expansion of e.g.f. exp(x / (1 - x^2)) / (1 - x^2).

1, 1, 3, 13, 61, 441, 3031, 28813, 267513, 3088081, 36278731, 491262861, 6962025973, 108395586313, 1791145742751, 31601369155021, 594291393830641, 11740929829286433, 246910933786777363, 5406641472165854221, 125497950720670828461, 3018786042678264770521

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

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

FORMULA

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

a(n) == 1 (mod 2).

PROG

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

CROSSREFS

Cf. A373681, A373682.