A249927 G.f. A(x) satisfies: 1+x = 2*A(x)^3 - A(x)^5.

1, 1, 4, 40, 485, 6585, 95732, 1457636, 22947585, 370494965, 6101028934, 102074877086, 1730213141683, 29649526507055, 512810063004600, 8940267160930408, 156944360941491106, 2771866193105829798, 49218079130561578390, 878107603236732844610, 15733529061871743649380

Offset: 0

Author

Paul D. Hanna, Nov 27 2014

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 4*x^2 + 40*x^3 + 485*x^4 + 6585*x^5 + 95732*x^6 +...
Related expansions.
A(x)^3 = 1 + 3*x + 15*x^2 + 145*x^3 + 1755*x^4 + 23793*x^5 +...
A(x)^5 = 1 + 5*x + 30*x^2 + 290*x^3 + 3510*x^4 + 47586*x^5 +...
where 1+x = 2*A(x)^3 - A(x)^5.
		

Crossrefs

Cf. A249926, A249928, A249929, A249930, A249931, A249932.

Programs

PARI

/* From 1+x = 2*A(x)^3 - A(x)^5: */
{a(n)=local(A=[1, 1]); for(i=1, n, A=concat(A, 0); A[#A]=-Vec(2*Ser(A)^3-Ser(A)^5)[#A]); A[n+1]}
for(n=0, 25, print1(a(n) , ", "))

PARI

/* From Series Reversion: */
{a(n)=local(A=1+serreverse(x - 4*x^2 - 8*x^3 - 5*x^4 - x^5 + x^2*O(x^n)));polcoeff(A,n)}
for(n=0, 25, print1(a(n) , ", "))

Formula

G.f.: 1 + Series_Reversion(x - 4*x^2 - 8*x^3 - 5*x^4 - x^5).