A227222 G.f. satisfies: A(x) = Sum{n>=0} A( n*x/(1-n*x) ) * x^n, with A(0)=1.

1, 1, 2, 6, 27, 172, 1508, 18107, 297532, 6694132, 206841391, 8816277300, 520844677834, 42854370882379, 4933351077116176, 797908056582772334, 181972606629594221271, 58701383528452842764544, 26853636463946258949427440, 17457976736153040916394583563

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

G.f.: Sum_{n>=0} x^n * Sum{k=0..n} a(k)*(n-k)^k/(1 - (n-k)*x)^k = Sum_{n>=0} a(n)*x^n.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 27*x^4 + 172*x^5 + 1508*x^6 +...
where
A(x) = 1 + A(x/(1-x))*x + A(2*x/(1-2*x))*x^2 + A(3*x/(1-3*x))*x^3 + A(4*x/(1-4*x))*x^4 + A(5*x/(1-5*x))*x^5 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, subst(A, x, m*x/(1-m*x+x*O(x^n)))*x^m)); polcoeff(A, n)}
for(n=0, 21, print1(a(n), ", "))

Crossrefs

Cf. A125282.

Sequence in context: A231934 A291979 A070076 * A370982 A130455 A372346

Adjacent sequences: A227219 A227220 A227221 * A227223 A227224 A227225

Keyword

nonn

Author

Paul D. Hanna, Sep 19 2013

Status

approved