A358852 a(n) = n!*Sum_{m=0..floor(n/3)} 1/binomial(n-m,2*m).

1, 1, 2, 12, 32, 140, 1512, 6384, 44928, 749088, 4299840, 42546240, 974695680, 7061783040, 90598072320, 2640888230400, 23099489280000, 364696083763200, 12881138586624000, 132004210918809600, 2475855534329856000, 102587486964092928000, 1205260977814806528000

Offset: 0

Author

Vladimir Kruchinin, Dec 02 2022

Keywords

• nonn

Links

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

Crossrefs

Cf. A358446.

Programs

Maxima

a(n):=n!*sum(1/(binomial(n-m,2*m)),m,0,floor(n/3));

PARI

a(n) = n!*sum(m=0, n\3, 1/binomial(n-m,2*m)); \\ Michel Marcus, Dec 03 2022

Formula

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