A277304 - OEIS

%I #9 Oct 25 2016 21:18:44

%S 1,6,84,1614,36948,947412,26334072,778107150,24133349532,778923367284,

%T 26000354998920,893459845502916,31496296778304936,1135911643635146712,

%U 41820127450763818896,1568983653501973667262,59898843849911992994340,2324166762372316001442540,91565378725229449617874824,3659689884915567083966937156,148284110214725433666804447912

%N G.f. satisfies: A(x - A(x)^2) = x + 5*A(x)^2.

%H Paul D. Hanna, <a href="/A277304/b277304.txt">Table of n, a(n) for n = 1..300</a>

%F G.f. A(x) also satisfies:

%F (1) A(x) = x + 6 * A( 5*x/6 + A(x)/6 )^2.

%F (2) A(x) = -5*x + 6 * Series_Reversion(x - A(x)^2).

%F (3) R(x) = -x/5 + 6/5 * Series_Reversion(x + 5*A(x)^2), where R(A(x)) = x.

%F (4) R( sqrt( x/6 - R(x)/6 ) ) = x/6 + 5*R(x)/6, where R(A(x)) = x.

%F a(n) = Sum_{k=0..n-1} A277295(n,k) * 6^(n-k-1).

%e G.f.: A(x) = x + 6*x^2 + 84*x^3 + 1614*x^4 + 36948*x^5 + 947412*x^6 + 26334072*x^7 + 778107150*x^8 + 24133349532*x^9 + 778923367284*x^10 +...

%o (PARI) {a(n) = my(A=[1], F=x); for(i=1, n, A=concat(A, 0); F=x*Ser(A); A[#A] = -polcoeff(subst(F, x, x - F^2) - 5*F^2, #A) ); A[n]}

%o for(n=1, 30, print1(a(n), ", "))

%Y Cf. A277295, A213591, A275765, A276360, A276361, A276362, A276363.

%Y Cf. A277300, A277301, A277302, A277303, A277305, A277306, A277307, A277308, A277309.

%Y Cf. A276364.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Oct 09 2016