A221988 G.f.: Sum_{n>=0} n! * (2*x)^n * Product_{k=1..n} (1 + k*x)/(1 + 2*k*x + 2*k^2*x^2).

1, 2, 6, 24, 116, 664, 4392, 32928, 276016, 2557856, 25965408, 286538112, 3415359296, 43727878528, 598510015104, 8720853182976, 134778021389056, 2202055694727680, 37923940767905280, 686639853639505920, 13038833241899856896, 259119925532534413312

Offset: 0

Author

Paul D. Hanna, Feb 02 2013

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 2*x + 6*x^2 + 24*x^3 + 116*x^4 + 664*x^5 + 4392*x^6 +...
where
A(x) = 1 + (2*x)*(1+x)/(1+2*x+2*x^2) + 2!*(2*x)^2*(1+x)*(1+2*x)/((1+2*x+2*x^2)*(1+4*x+8*x^2)) + 3!*(2*x)^3*(1+x)*(1+2*x)*(1+3*x)/((1+2*x+2*x^2)*(1+4*x+8*x^2)*(1+6*x+18*x^2)) + 4!*(2*x)^4*(1+x)*(1+2*x)*(1+3*x)*(1+4*x)/((1+2*x+2*x^2)*(1+4*x+8*x^2)*(1+6*x+18*x^2)*(1+8*x+32*x^2)) +...
		

Crossrefs

Cf. A221987, A208237, A136127, A221973.

Programs

PARI

{a(n)=polcoeff( sum(m=0, n, m!*(2*x)^m*prod(k=1, m, (1+k*x)/(1+2*k*x+2*k^2*x^2 +x*O(x^n))) ), n)}
for(n=0, 25, print1(a(n), ", "))