A208831 G.f.: 1/(1-x) = Sum_{n>=0} a(n) * x^n / Product_{k=1..2*n} (1 + k*x).

1, 1, 4, 34, 470, 9246, 239254, 7735818, 301515326, 13798284326, 726653380406, 43347208596090, 2892081998352630, 213573932091190350, 17305963353368021974, 1527409032389494461130, 145910774659458343922094, 15004445714376212721001782, 1653029709428208769065420054

Offset

0,3

Comments

Compare g.f. to: 1/(1-x) = Sum_{n>=0} n!*x^n/Product_{k=1..n} (1 + k*x).

Links

Table of n, a(n) for n=0..18.

Example

 G.f.: 1/(1-x) = 1 + 1*x/((1+x)*(1+2*x)) + 4*x^2/((1+x)*(1+2*x)*(1+3*x)*(1+4*x)) + 34*x^3/((1+x)*(1+2*x)*(1+3*x)*(1+4*x)*(1+5*x)*(1+6*x)) + 470*x^4/((1+x)*(1+2*x)*(1+3*x)*(1+4*x)*(1+5*x)*(1+6*x)*(1+7*x)*(1+8*x)) +...

Prog

 (PARI) {a(n)=if(n==0, 1, 1-polcoeff(sum(k=0, n-1, a(k)*x^k/prod(j=1, 2*k, (1+j*x+x*O(x^n)) )), n))}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A208830.

Sequence in context: A234291 A193099 A368445 * A294475 A198976 A156325

Adjacent sequences: A208828 A208829 A208830 * A208832 A208833 A208834

Keyword

nonn

Author

Paul D. Hanna, Mar 01 2012

Status

approved