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A153852 Nonzero coefficients of g.f.: A(x) = G(G(x)) where G(x) = x + G(G(x))^3 is the g.f. of A153851. 4
1, 2, 15, 165, 2213, 33693, 561867, 10053141, 190489374, 3788856192, 78613758564, 1693737431667, 37760673462507, 868775517322730, 20583609967109565, 501340716386677815, 12535093359045980151, 321360932709750239226 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..18.

FORMULA

G.f.: A(x) = Sum_{n>=0} a(2n+1)*x^(2n+1) = G(G(x)) where G(x) is the g.f. of A153851.

G.f.: A(x) = G(x) + H(x)^3 where G(x) is the g.f. of A153851 and H(x) is the g.f. of A153853.

EXAMPLE

G.f.: A(x) = x + 2*x^3 + 15*x^5 + 165*x^7 + 2213*x^9 +...

A(x)^3 = x^3 + 6*x^5 + 57*x^7 + 683*x^9 + 9474*x^11 + 145815*x^13 +...

A(x) = G(G(x)) where

G(x) = x + x^3 + 6*x^5 + 57*x^7 + 683*x^9 + 9474*x^11 +...

Let H(x) = g.f. of A153853, then A(x) = G(x) + H(x)^3 where

H(x) = x + 3*x^3 + 27*x^5 + 339*x^7 + 5067*x^9 + 84738*x^11 +...

H(x)^3 = x^3 + 9*x^5 + 108*x^7 + 1530*x^9 + 24219*x^11 +...

PROG

(PARI) {a(n)=local(G=x+O(x^(2*n+1))); for(i=0, n, G=serreverse(x-G^3)); polcoeff(subst(G, x, G), 2*n-1)}

CROSSREFS

Cf. A153851, A153853, A153854, A153850.

Sequence in context: A259608 A317278 A140809 * A177396 A324151 A262035

Adjacent sequences:  A153849 A153850 A153851 * A153853 A153854 A153855

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 21 2009

EXTENSIONS

Formula corrected by Paul D. Hanna, Dec 07 2009

STATUS

approved

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Last modified December 6 04:20 EST 2021. Contains 349562 sequences. (Running on oeis4.)