A156335 G.f.: A(x) = exp( Sum_{n>=1} 2^[(n^2+1)/2]*x^n/n ), a power series in x with integer coefficients.

1, 2, 4, 16, 92, 1816, 47344, 4888640, 546663016, 245429690704, 113080892367776, 209848258185362560, 393950238751186551328, 2976605303522286162203456, 22642571073509592590956639360, 692351532949951721637759480882688

Offset

0,2

Links

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

Formula

a(n) = (1/n)*Sum_{k=1..n} 2^floor((k^2+1)/2) * a(n-k) for n>0, with a(0)=1.

Example

G.f.: A(x) = 1 + 2*x + 4*x^2 + 16*x^3 + 92*x^4 + 1816*x^5 + 47344*x^6 +...
log(A(x)) = 2*x + 2^2*x^2/2 + 2^5*x^3/3 + 2^8*x^4/4 + 2^13*x^5/5 + 2^18*x^6/6 +...

Prog

(PARI) {a(n)=polcoeff(exp(sum(k=1, n, 2^floor((k^2+1)/2)*x^k/k)+x*O(x^n)), n)}

Crossrefs

Cf. A156334, A156336, A156337, A155200.

Sequence in context: A291286 A007171 A058136 * A026089 A052835 A009565

Adjacent sequences: A156332 A156333 A156334 * A156336 A156337 A156338

Keyword

nonn

Author

Paul D. Hanna, Feb 10 2009

Status

approved