A358791 a(n) = n!*Sum_{m=0..floor(n/2)} binomial(n,2*m)^(-1).

1, 1, 4, 8, 52, 156, 1536, 6144, 84096, 420480, 7453440, 44720640, 974972160, 6824805120, 176504832000, 1412038656000, 42224136192000, 380017225728000, 12893605517721600, 128936055177216000, 4892595136708608000

Offset: 0

Author

Vladimir Kruchinin, Dec 01 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..449

Crossrefs

Cf. A003149.

Programs

Maxima

a(n):=n!*sum(1/binomial(n,2*m),m,0,floor(n/2));

PARI

a(n) = n!*sum(m=0, n\2, 1/binomial(n, 2*m)); \\ Michel Marcus, Dec 01 2022

Formula

E.g.f.: (1/2)*( log(1+x)/x^2-log(1-x)*(x^2+4*x-4)/(x^4-4*x^3+4*x^2)+6/(x^3-2*x^2-x+2) ).

P-recursive: 2*n*(n + 2)*(n - 2)*(3*n - 2)*a(n) = n*(n + 1)*(n + 2)*(n - 2)*(3*n - 2)*a(n-1) + 2*n^3*(n - 1)*(n - 2)*(3*n + 4)*a(n-2) - n^3*(n - 1)^2*(n - 2)*(3*n + 4)*a(n-3) with a(0) = a(1) = 1 and a(2) = 4. - Peter Bala, Apr 13 2023