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A179467 G.f. satisfies: A(x) = exp( Sum_{n>=1} sigma(n)*A(x^n)*x^n/n ). 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 18 04:22 EDT 2021. Contains 347508 sequences. (Running on oeis4.)