A134529 E.g.f. A(x) satisfies: x/(1-x)^2 = Sum_{n>=1} (1/n!)*Product_{j=0..n-1} A(2^j*x).

0, 1, 2, -8, -80, 1576, 43056, -4001376, -539274240, 230311875456, 169101315797760, -333305191377561600, -1205460382028665927680, 11038562078873652773729280, 187384458453666330945406187520, -7882186562442515869956999642009600

Offset

0,3

Links

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

Formula

Define F(x,k,m) = Sum_{n>=1} (m*2^k)^n/n! * Product_{j=0..n-1} A(2^j*x), then F(x,k,m) is a series in x with integer coefficients for all integer m, k>=0.

Example

E.g.f.: A(x) = x + 2x^2/2! - 8x^3/3! - 80x^4/4! + 1576x^5/5! + 43056x^6/6! + ...
where A(x) satisfies:
x/(1-x)^2 = A(x) + A(x)*A(2*x)/2! + A(x)*A(2*x)*A(2^2*x)/3! + A(x)*A(2*x)*A(2^2*x)*A(2^3*x)/4! + ...

Prog

(PARI) {a(n, q=2)=local(A=x/(1-x+x*O(x^n))^2); for(i=1, n, A=x/(1-x)^2/(1+sum(j=1, n, prod(k=1, j, subst(A, x, q^k*x))/(j+1)!))); return(n!*polcoeff(A, n))}

Crossrefs

Sequence in context: A202999 A308088 A130530 * A289897 A134054 A323716

Adjacent sequences: A134526 A134527 A134528 * A134530 A134531 A134532

Keyword

sign

Author

Paul D. Hanna, Nov 23 2007

Status

approved