A116400 E.g.f. Bessel_I(2,2x)+Bessel_I(3,2x)+Bessel_I(4,2x).

0, 0, 1, 1, 5, 5, 21, 21, 84, 84, 330, 330, 1287, 1287, 5005, 5005, 19448, 19448, 75582, 75582, 293930, 293930, 1144066, 1144066, 4457400, 4457400, 17383860, 17383860, 67863915, 67863915, 265182525

Offset: 0

Author

Paul Barry, Feb 13 2006

Keywords

• easy
• nonn

Comments

T(n,2) in number triangle A116399. Double of A002054.

Crossrefs

A002054(n)=a(2n)=a(2n+1).

Programs

PARI

a(n)=n=n\2; binomial(2*n+1,n-1)

Formula

G.f.: (1+x)*x^2*c(x^2)^4/(2-c(x^2)), c(x) the g.f. of A000108; a(n)=C(n+1,n/2-1)(1+(-1)^n)/2 + C(n,(n-1)/2-1)(1-(-1)^n)/2.