A136554 G.f.: A(x) = Sum_{n>=0} log( (1 + x)*(1 + 2^n*x) )^n / n!.

1, 3, 10, 82, 2304, 232088, 81639942, 99425060368, 421915147527984, 6313762292901492960, 337457827116687464134048, 65175276571204939272971781496, 45944813538624773942727094008288680

Offset

0,2

Links

Table of n, a(n) for n=0..12.

Formula

a(n) = Sum_{k=0..n} C(2^k, k)*C(2^k, n-k).

G.f.: A(x) = Sum_{n>=0} C(2^n,n) * x^n * (1+x)^(2^n).

Example

G.f.: A(x) = 1 + 3*x + 10*x^2 + 82*x^3 + 2304*x^4 + 232088*x^5 +...;
A(x) = 1 + log((1+x)*(1+2*x)) + log((1+x)*(1+4*x))^2/2! + log((1+x)*(1+8*x))^3/3! + log((1+x)*(1+16*x))^4/4! +...
Surprisingly, this sum yields a series in x with only integer coefficients.

Prog

(PARI) {a(n)=polcoeff(sum(i=0, n, log((1+x)*(1+2^i*x)+x*O(x^n))^i/i!), n)}
(PARI) {a(n)=sum(k=0, n, binomial(2^k, k)*binomial(2^k, n-k))}

Crossrefs

Sequence in context: A262259 A203492 A320258 * A359970 A341848 A136505

Adjacent sequences: A136551 A136552 A136553 * A136555 A136556 A136557

Keyword

nonn

Author

Paul D. Hanna, Jan 06 2008, Jan 07 2008

Status

approved