A225294 G.f. satisfies: A(x) = Sum_{n>=0} x^n / Product_{k=1..n} (1 - k*x*A(x)).

1, 1, 2, 6, 22, 92, 424, 2112, 11236, 63360, 376800, 2355016, 15430784, 105797968, 757866592, 5664174736, 44109816528, 357447744576, 3010091812000, 26304829992224, 238217024498432, 2232483865359488, 21621812897089536, 216130222764401024, 2226983944005048960

Offset

0,3

Comments

It appears that all terms a(n) for n>1 are even.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..154

Formula

G.f. satisfies: A(x) = Sum_{n>=0} x^n * Sum_{k=0..n} Stirling2(n,k)*A(x)^(n-k).

Example

G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 22*x^4 + 92*x^5 + 424*x^6 + 2112*x^7 +...
where
A(x) = 1 + x/(1-x*A(x)) + x^2/((1-x*A(x))*(1-2*x*A(x))) + x^3/((1-x*A(x))*(1-2*x*A(x))*(1-3*x*A(x))) + x^4/((1-x*A(x))*(1-2*x*A(x))*(1-3*x*A(x))*(1-4*x*A(x))) +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, x^m/prod(k=1, m, 1-k*x*A +x*O(x^n)) )); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
(PARI) {Stirling2(n, k)=n!*polcoeff(((exp(x+x*O(x^n))-1)^k)/k!, n)}
{a(n)=local(A=1+x); for(i=0, n, A=sum(m=0, n, x^m*sum(k=0, m, Stirling2(m, k)*(A+x*O(x^n))^(m-k)))); polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A224922, A225293, A000110, A019538.

Sequence in context: A107945 A279571 A014330 * A124294 A124295 A074664

Adjacent sequences: A225291 A225292 A225293 * A225295 A225296 A225297

Keyword

nonn

Author

Paul D. Hanna, May 04 2013

Status

approved