A221586 G.f. satisfies: A(x) = Sum_{n>=0} x^n * A(x)^(n*(n+1)/2) / Product_{k=1..n} (1 + x*A(x)^k).

1, 1, 1, 2, 5, 14, 43, 140, 478, 1695, 6205, 23356, 90135, 355960, 1436755, 5922799, 24929035, 107136291, 470281976, 2109608447, 9677546281, 45434467501, 218478232454, 1076855324959, 5443845581547, 28239060235110, 150346623540441, 821555490484095

Offset

0,4

Links

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

Example

G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 5*x^4 + 14*x^5 + 43*x^6 + 140*x^7 +...
where
A(x) = 1 + x*A(x)/(1+x*A(x)) + x^2*A(x)^3/((1+x*A(x))*(1+x*A(x)^2)) + x^3*A(x)^6/((1+x*A(x))*(1+x*A(x)^2)*(1+x*A(x)^3)) + x^4*A(x)^10/((1+x*A(x))*(1+x*A(x)^2)*(1+x*A(x)^3)*(1+x*A(x)^4)) +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, x^m*A^(m*(m+1)/2)/prod(k=1, m, 1+x*subst(A, x, x+x*O(x^n))^k))); polcoeff(A, n)}; \\ corrected by Georg Fischer, Jun 20 2022

Crossrefs

Cf. A221547, A221585.

Sequence in context: A213264 A029889 A307787 * A258312 A123020 A005317

Adjacent sequences: A221583 A221584 A221585 * A221587 A221588 A221589

Keyword

nonn

Author

Paul D. Hanna, Jan 20 2013

Status

approved