A277304 G.f. satisfies: A(x - A(x)^2) = x + 5*A(x)^2.

1, 6, 84, 1614, 36948, 947412, 26334072, 778107150, 24133349532, 778923367284, 26000354998920, 893459845502916, 31496296778304936, 1135911643635146712, 41820127450763818896, 1568983653501973667262, 59898843849911992994340, 2324166762372316001442540, 91565378725229449617874824, 3659689884915567083966937156, 148284110214725433666804447912

Offset

1,2

Links

Paul D. Hanna, Table of n, a(n) for n = 1..300

Formula

G.f. A(x) also satisfies:

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

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

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

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

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

Example

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 +...

Prog

(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]}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

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

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

Cf. A276364.

Sequence in context: A113888 A163947 A306244 * A128575 A369531 A322518

Adjacent sequences: A277301 A277302 A277303 * A277305 A277306 A277307

Keyword

nonn

Author

Paul D. Hanna, Oct 09 2016

Status

approved