A113327 a(n) = Sum_{k=0..n} 2^k*A111146(n,k).

1, 2, 8, 36, 176, 928, 5296, 33024, 227776, 1757504, 15269888, 149327616, 1632715520, 19758502912, 261836047360, 3763432774656, 58208166178816, 962637398577152, 16934963591229440, 315578267054112768

Offset: 0

Author

Philippe Deléham and Paul D. Hanna, Oct 26 2005

Keywords

• nonn

Examples

			A(x) = (1 + 2*x + 8*x^2 + 36*x^3 + 176*x^4 + 928*x^5 +..) =
1/(1 - 2/1!*x*(1! + 2!*x + 3!*x^2 + 4!*x^3 + 5!*x^4 +..) ).
		

Crossrefs

Cf. A111146, A113326, A113328 (y=3), A113329 (y=4), A113330 (y=5), A113331 (y=6).

Programs

PARI

{a(n)=local(y=2,x=X+X*O(X^n)); polcoeff(1/(1 - y/(y-1)!*x*sum(k=0,n,(y-1+k)!*x^k)),n,X)}

Formula

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