A102223 Column 0 of triangular matrix A102222, which equals -log[2*I - A008459].

0, 1, 3, 22, 323, 7906, 290262, 14919430, 1022475715, 90094491994, 9923239949978, 1335853771297750, 215797095378591542, 41198645313603207990, 9176288655853717238830, 2358300288047799986966722

Offset

0,3

Comments

Triangle A008459 consists of squared binomial coefficients.

Links

Table of n, a(n) for n=0..15.

Formula

a(n) = 1 + (1/n)*Sum_{k=0..n-1} C(n, k)^2*k*a(k) for n>0, with a(0)=0.

Sum_{n>=0} a(n)*x^n/n!^2 = -log(2-BesselI(0,2*sqrt(x))). - Vladeta Jovovic, Jul 16 2006

Example

a(2) = 3 = 1 + (1*0*0 + 4*1*1)/2,
a(3) = 22 = 1 + (1*0*0 + 9*1*1 + 9*2*3)/3,
a(4) = 323 = 1 + (1*0*0 + 16*1*1 + 36*2*3 + 16*3*22)/4,
a(5) = 7906 = 1 + (1*0*0 + 25*1*1 + 100*2*3 + 100*3*22 + 25*4*323)/5.

Prog

(PARI) a(n)=if(n<1, 0, 1+sum(k=0, n-1, binomial(n, k)^2*k*a(k))/n)

Crossrefs

Cf. A008459, A102220, A102222.

Sequence in context: A161967 A192036 A229770 * A189897 A306578 A046947

Adjacent sequences: A102220 A102221 A102222 * A102224 A102225 A102226

Keyword

nonn

Author

Paul D. Hanna, Dec 31 2004

Status

approved