A153854 - OEIS

%I #6 Oct 05 2024 16:30:04

%S 1,4,42,594,9827,179928,3545637,73988631,1618178067,36832568283,

%T 868184365137,21113629246953,528282055072773,13569770211307323,

%U 357215846155083585,9623529095387448543,265025641890780905892

%N Nonzero coefficients of g.f.: A(x) = G(G(G(G(x)))) where G(x) = x + G(G(x))^3 is the g.f. of A153851.

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

%F G.f.: A(x) = F(F(x)) where F(x) is the g.f. of A153852.

%e G.f.: A(x) = x + 4*x^3 + 42*x^5 + 594*x^7 + 9827*x^9 +...

%e A(x)^3 = x^3 + 12*x^5 + 174*x^7 + 2854*x^9 + 51045*x^11 +...

%e A(x) = G(G(G(G(x)))) where

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

%e A(x) = F(F(x)) where F(x) = G(G(x)) is the g.f. of A153852:

%e F(x) = x + 2*x^3 + 15*x^5 + 165*x^7 + 2213*x^9 + 33693*x^11 +...

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

%Y Cf. A153851, A153852, A153853, A153850.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Jan 21 2009