A179467 G.f. satisfies: A(x) = exp( Sum_{n>=1} sigma(n)*A(x^n)*x^n/n ).

1, 1, 3, 7, 19, 47, 131, 351, 992, 2808, 8131, 23723, 70192, 209209, 629165, 1904391, 5801109, 17764063, 54663309, 168925259, 524064687, 1631511342, 5095440198, 15960070908, 50124189982, 157806721089, 497953049736, 1574573746276

Offset

0,3

Links

Table of n, a(n) for n=0..27.

Formula

G.f.: Sum_{n>=0} a(n)*x^n = Product_{n>=1} P(x^n)^a(n-1) where P(x) = Product_{k>=1} 1/(1-x^k) is the partition function.

Example

G.f.: A(x) = 1 + x + 3*x^2 + 7*x^3 + 19*x^4 + 47*x^5 + 131*x^6 +...
log(A(x)) = A(x)*x + 3*A(x^2)*x^2/2 + 4*A(x^3)*x^3/3 + 7*A(x^4)*x^4/4 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, subst(A, x, x^m+x*O(x^n))*sigma(m)*x^m/m))); polcoeff(A, n)}
(PARI) {a(n)=if(n<0, 0, if(n==0, 1, polcoeff(1/prod(m=1, n, prod(k=1, n\m+1, 1-x^(k*m)+x*O(x^n))^a(m-1)), n)))}

Crossrefs

Sequence in context: A151535 A181360 A001372 * A308153 A049117 A146810

Adjacent sequences: A179464 A179465 A179466 * A179468 A179469 A179470

Keyword

nonn

Author

Paul D. Hanna, Jul 15 2010

Status

approved