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A193194 G.f. satisfies: A(A(x)) = Sum_{n>=1} a(n)*x^n * (1+x)^(n*(n+1)/2), where g.f. A(x) = Sum_{n>=1} a(n)*x^n. 4
1, 1, 1, 3, 20, 262, 5367, 158413, 6318384, 326575077, 21199737973, 1687053244236, 161418184139781, 18276066372054109, 2416167457088427950, 368773198369779785338, 64348161941454274119082, 12728047101293068225626576, 2832615019902477894227329544 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..19.

EXAMPLE

G.f.: A(x) = x + x^2 + x^3 + 3*x^4 + 20*x^5 + 262*x^6 + 5367*x^7 +...

where

A(A(x)) = x*(1+x) + x^2*(1+x)^3 + x^3*(1+x)^6 + 3*x^4*(1+x)^10 + 20*x^5*(1+x)^15 + 262*x^6*(1+x)^21 +...+ a(n)*x^n*(1+x)^(n*(n+1)/2) +...

Explicitly,

A(A(x)) = x + 2*x^2 + 4*x^3 + 12*x^4 + 66*x^5 + 717*x^6 + 13344*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*(m+1)/2));

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

CROSSREFS

Cf. A193192, A193193, A193195.

Sequence in context: A197322 A197975 A210906 * A320945 A166232 A136551

Adjacent sequences:  A193191 A193192 A193193 * A193195 A193196 A193197

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 19 2011

STATUS

approved

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Last modified October 19 22:00 EDT 2021. Contains 348095 sequences. (Running on oeis4.)