A249928 G.f. A(x) satisfies: 1+x = A(x)^2 + A(x)^5 - A(x)^6.

1, 1, 4, 42, 530, 7489, 113289, 1794784, 29397876, 493818165, 8460325159, 147264321834, 2596986868762, 46299572773077, 833111268412360, 15110637698827976, 275970530427257207, 5070759797283817869, 93671715612197557390, 1738657226550598494420, 32409645286487921390715

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

G.f.: 1 + Series_Reversion(x - 4*x^2 - 10*x^3 - 10*x^4 - 5*x^5 - x^6).

Example

 G.f.: A(x) = 1 + x + 4*x^2 + 42*x^3 + 530*x^4 + 7489*x^5 + 113289*x^6 +...
Related expansions.
A(x)^2 = 1 + 2*x + 9*x^2 + 92*x^3 + 1160*x^4 + 16374*x^5 +...
A(x)^5 = 1 + 5*x + 30*x^2 + 300*x^3 + 3775*x^4 + 53226*x^5 +...
A(x)^6 = 1 + 6*x + 39*x^2 + 392*x^3 + 4935*x^4 + 69600*x^5 +...
where 1+x = A(x)^2 + A(x)^5 - A(x)^6.

Prog

 (PARI) /* From 1+x = A(x)^2 + A(x)^5 - A(x)^6: */
{a(n)=local(A=[1, 1]); for(i=1, n, A=concat(A, 0); A[#A]=-Vec(Ser(A)^2+Ser(A)^5-Ser(A)^6)[#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 - 10*x^3 - 10*x^4 - 5*x^5 - x^6 + x^2*O(x^n))); polcoeff(A, n)}
for(n=0, 25, print1(a(n) , ", "))

Crossrefs

Cf. A249926, A249927, A249929, A249930, A249931, A249932.

Sequence in context: A092800 A370282 A268542 * A156440 A151453 A234507

Adjacent sequences: A249925 A249926 A249927 * A249929 A249930 A249931

Keyword

nonn

Author

Paul D. Hanna, Nov 27 2014

Status

approved