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A193193 G.f. satisfies: A(A(x)) = Sum_{n>=1} a(n)*x^n / (1-x)^(n^2), where g.f. A(x) = Sum_{n>=1} a(n)*x^n. 4
1, 1, 3, 22, 334, 8831, 359836, 20845201, 1625007715, 163854289212, 20739421240200, 3218400384155498, 600776969761195428, 132793055529329858607, 34298178516935957467888, 10235014757932193318825335 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..16.

EXAMPLE

G.f.: A(x) = x + x^2 + 3*x^3 + 22*x^4 + 334*x^5 + 8831*x^6 +...

where

A(A(x)) = x/(1-x) + x^2/(1-x)^4 + 3*x^3/(1-x)^9 + 22*x^4/(1-x)^16 + 334*x^5/(1-x)^25 + 8831*x^6/(1-x)^36 +...+ a(n)*x^n/(1-x)^(n^2) +...

Explicitly,

A(A(x)) = x + 2*x^2 + 8*x^3 + 60*x^4 + 842*x^5 + 20704*x^6 + 805796*x^7 +...

PROG

(PARI) {a(n)=local(A=[1], F=x, G=x); for(i=1, n, A=concat(A, 0); F=x*Ser(A);

G=sum(m=1, #A-1, A[m]*x^m/(1-x+x*O(x^#A))^(m^2));

A[#A]=Vec(G)[#A]-Vec(subst(F, x, F))[#A]); if(n<1, 0, A[n])}

CROSSREFS

Cf. A193192, A193194, A193195.

Sequence in context: A306578 A046947 A002485 * A099750 A219268 A259919

Adjacent sequences:  A193190 A193191 A193192 * A193194 A193195 A193196

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 19 2011

STATUS

approved

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Last modified December 9 08:41 EST 2021. Contains 349627 sequences. (Running on oeis4.)