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A225293 G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^n / Product_{k=1..n} (1 - k*x). 4
1, 1, 3, 11, 46, 210, 1022, 5232, 27954, 155142, 892007, 5306785, 32662475, 208108337, 1374219242, 9418564346, 67102315232, 497617712664, 3844733673180, 30960923835040, 259797722635505, 2269726236363395, 20618932709111866, 194452174592422916, 1900387863379327247 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..219

FORMULA

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

EXAMPLE

G.f.: A(x) = 1 + x + 3*x^2 + 11*x^3 + 46*x^4 + 210*x^5 + 1022*x^6 +...

where

A(x) = 1 + x*A(x)/(1-x) + x^2*A(x)^2/((1-x)*(1-2*x)) + x^3*A(x)^3/((1-x)*(1-2*x)*(1-3*x)) + x^4*A(x)^4/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)) +...

PROG

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

for(n=0, 20, 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))^k))); polcoeff(A, n)}

for(n=0, 20, print1(a(n), ", "))

CROSSREFS

Cf. A224922, A225294, A000110, A019538.

Sequence in context: A233389 A281548 A086521 * A046996 A248426 A129579

Adjacent sequences:  A225290 A225291 A225292 * A225294 A225295 A225296

KEYWORD

nonn

AUTHOR

Paul D. Hanna, May 04 2013

STATUS

approved

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Last modified October 16 16:16 EDT 2019. Contains 328101 sequences. (Running on oeis4.)