A187827 G.f. satisfies: A(x) = Sum_{n>=0} (1 - (1 - x*A(x))^n)^n.

1, 1, 5, 36, 325, 3468, 42519, 590268, 9201740, 160150252, 3095440553, 66068011710, 1547572760559, 39529002357409, 1094096683131616, 32622859912512090, 1042350065213470532, 35521574976088978133, 1285782300453328211074, 49256935742079848796102

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..140

Formula

G.f. satisfies: A(x) = Sum_{n>=1} (1-x*A(x))^n * (1 - (1-x*A(x))^n)^(n-1).

a(n) ~ c * n^n / (exp(n) * (log(2))^(2*n)), where c = 3.7860088... . - Vaclav Kotesovec, Nov 08 2014

Example

G.f.: A(x) = 1 + x + 5*x^2 + 36*x^3 + 325*x^4 + 3468*x^5 + 42519*x^6 +...
where the g.f. satisfies the identities:
(1) A(x) = 1 + x*A(x) + (1 - (1-x*A(x))^2)^2 + (1 - (1-x*A(x))^3)^3 + (1 - (1-x*A(x))^4)^4 + (1 - (1-x*A(x))^5)^5 +...
(2) A(x) = (1-x*A(x)) + (1-x*A(x))^2*(1 - (1-x*A(x))^2) + (1-x*A(x))^3*(1 - (1-x*A(x))^3)^2 + (1-x*A(x))^4*(1 - (1-x*A(x))^4)^3 + (1-x)^5*(1 - (1-x*A(x))^5)^4 +...

Prog

(PARI) {a(n)=local(q, A=1); for(i=1, n, q=1/(1-x*A+x*O(x^n)); A=sum(k=0, n+1, q^(-k^2)*(q^k-1)^k)); polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))
(PARI) {a(n)=local(q, A=1); for(i=1, n, q=1/(1-x*A+x*O(x^n)); A=sum(k=1, n+1, q^(-k^2)*(q^k-1)^(k-1))); polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A220353, A187826.

Sequence in context: A278576 A286765 A267980 * A291688 A300987 A067305

Adjacent sequences: A187824 A187825 A187826 * A187828 A187829 A187830

Keyword

nonn

Author

Paul D. Hanna, Dec 27 2012

Status

approved