A249930 G.f. A(x) satisfies: 1+x = A(x)^2 + A(x)^6 - A(x)^7.

1, 1, 5, 65, 1020, 17915, 336881, 6634391, 135085305, 2820748975, 60074608660, 1299896748546, 28496343865808, 631545920570632, 14126673078922850, 318514279669755470, 7231331734648562366, 165172699475903928921, 3793005825337785580290, 87518313783310367308770

Offset: 0

Author

Paul D. Hanna, Nov 27 2014

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 5*x^2 + 65*x^3 + 1020*x^4 + 17915*x^5 + ...
Related expansions.
A(x)^2 = 1 + 2*x + 11*x^2 + 140*x^3 + 2195*x^4 + 38520*x^5 + ...
A(x)^6 = 1 + 6*x + 45*x^2 + 560*x^3 + 8760*x^4 + 153546*x^5 + ...
A(x)^7 = 1 + 7*x + 56*x^2 + 700*x^3 + 10955*x^4 + 192066*x^5 + ...
where 1+x = A(x)^2 + A(x)^6 - A(x)^7.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..700

Crossrefs

Cf. A249926, A249927, A249928, A249929, A249931, A249932.

Programs

Maple

S:= series(RootOf(1+x-(y^2+y^6-y^7),y,1),x,26):
seq(coeff(S,x,i),i=0..25); # Robert Israel, Mar 22 2023

PARI

/* From 1+x = A(x)^2 + A(x)^6 - A(x)^7: */
{a(n)=local(A=[1, 1]); for(i=1, n, A=concat(A, 0); A[#A]=-Vec(Ser(A)^2+Ser(A)^6-Ser(A)^7)[#A]); A[n+1]}
for(n=0, 25, print1(a(n) , ", "))

PARI

/* From Series Reversion: */
{a(n)=local(A=1+serreverse(x - 5*x^2 - 15*x^3 - 20*x^4 - 15*x^5 - 6*x^6 - x^7 + x^2*O(x^n)));polcoeff(A,n)}
for(n=0, 25, print1(a(n) , ", "))

Formula

G.f.: 1 + Series_Reversion(x - 5*x^2 - 15*x^3 - 20*x^4 - 15*x^5 - 6*x^6 - x^7).