A158097 G.f.: A(x) = exp( Sum_{n>=1} x^n/n * 2^(n^2)/(1 - 2^(n^2)*x^n) ).

1, 2, 14, 204, 16982, 6746636, 11467009772, 80444425963128, 2306004014991374374, 268654794950955551450892, 126765597355485863873077402788, 241678070949320869650125781001909864

Offset

0,2

Comments

Compare to g.f. of the partition numbers A000041:

exp( Sum_{n>=1} x^n/(1 - x^n)/n ) = 1 + x + 2*x^2 + 3*x^3 + 5*x^4 +...

Links

Table of n, a(n) for n=0..11.

Formula

G.f.: exp( Sum_{n>=1} x^n/n * Sum_{d|n} 2^(n*d) * n/d ).

Example

G.f.: A(x) = 1 + 2*x + 14*x^2 + 204*x^3 + 16982*x^4 + 6746636*x^5 +...
log(A(x)) = 2*x + 24*x^2/2 + 536*x^3/3 + 66112*x^4/4 + 33554592*x^5/5 +...
log(A(x)) = 2*x/(1-2*x) + 2^4*x^2/(1-2^4*x^2)/2 + 2^9*x^3/(1-2^9*x^3)/3 +...

Prog

(PARI) {a(n)=if(n==0, 1, polcoeff(exp(sum(k=1, n, (2^k*x)^k/(1-(2^k*x)^k +x*O(x^n))/k)), n))}
for(n=0, 15, print1(a(n), ", "))
(PARI) {a(n) = polcoeff( exp( sum(m=1, n, x^m/m * sumdiv(m, d, 2^(m*d) * m/d) ) +x*O(x^n)), n)}
for(n=0, 15, print1(a(n), ", ")) \\ Paul D. Hanna, Sep 30 2015

Crossrefs

Cf. A158096, A155200.

Sequence in context: A262008 A054652 A122647 * A262003 A271847 A136550

Adjacent sequences: A158094 A158095 A158096 * A158098 A158099 A158100

Keyword

nonn

Author

Paul D. Hanna, Mar 26 2009

Status

approved