A177778 E.g.f.: A(x) = Sum_{n>=0} 2^n/n!*Product_{k=0..n-1} L(2^k*x), where L(x) is the e.g.f. of A177777.

1, 2, 12, 160, 4272, 221648, 22347648, 4416360160, 1724182065408, 1336677590208512, 2064038664552586752, 6359502604300426739200, 39136760890428640414851072, 481344480930558145524346370048

Offset

0,2

Links

Table of n, a(n) for n=0..13.

Example

E.g.f.: A(x) = 1 + 2*x + 12*x^2/2! + 160*x^3/3! + 4272*x^4/4! +...
Then e.g.f. A(x) is given by:
A(x) = 1 + 2*L(x) + 2^2*L(x)L(2x)/2! + 2^3*L(x)L(2x)L(4x)/3! + 2^4*L(x)L(2x)L(4x)L(8x)/4! +...
where L(x) is the e.g.f. of A177777:
. L(x) = x + 2*x^2/2! + 12*x^3/3! + 152*x^4/4! + 3640*x^5/5! +...
. L(x) = x*d/dx log( Sum_{n>=0} 2^(n(n-1)/2)*x^n/n! )
and satisfies:
. L(x)/x = 1 + L(x) + L(x)L(2x)/2! + L(x)L(2x)L(4x)/3! + L(x)L(2x)L(4x)L(8x)/4! +...

Prog

(PARI) {a(n, q=2)=local(Lq=x+x^2, A); for(i=1, n, Lq=x*sum(m=0, n, (q-1)^m/m!*prod(k=0, m-1, subst(Lq, x, q^k*x+x*O(x^n))))); A=sum(m=0, n, 2^m/m!*prod(k=0, m-1, subst(Lq, x, q^k*x+x*O(x^n)))); n!*polcoeff(A, n)}

Crossrefs

Cf. A177777, A177780.

Sequence in context: A326222 A208577 A012646 * A180420 A012328 A302688

Adjacent sequences: A177775 A177776 A177777 * A177779 A177780 A177781

Keyword

nonn

Author

Paul D. Hanna, May 20 2010

Status

approved