A249932 G.f. A(x) satisfies: 1+x = 2*A(x)^4 - A(x)^7.

1, 1, 9, 189, 4893, 141771, 4399549, 143008579, 4806584226, 165685071354, 5825261477574, 208089042731934, 7531002619598458, 275548081670765638, 10175724606458649366, 378783118623851279250, 14197727780171976218883, 535401733845392629890255, 20298674469757725391376887

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

G.f.: 1 + Series_Reversion(x - 9*x^2 - 27*x^3 - 33*x^4 - 21*x^5 - 7*x^6 - x^7).

Example

 G.f.: A(x) = 1 + x + 9*x^2 + 189*x^3 + 4893*x^4 + 141771*x^5 +...
Related expansions.
A(x)^4 = 1 + 4*x + 42*x^2 + 868*x^3 + 22435*x^4 + 649488*x^5 +...
A(x)^7 = 1 + 7*x + 84*x^2 + 1736*x^3 + 44870*x^4 + 1298976*x^5 +...
where 1+x = 2*A(x)^4 - A(x)^7.

Prog

 (PARI) /* From 1+x = 2*A(x)^4 - A(x)^7: */
{a(n)=local(A=[1, 1]); for(i=1, n, A=concat(A, 0); A[#A]=-Vec(2*Ser(A)^4-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 - 9*x^2 - 27*x^3 - 33*x^4 - 21*x^5 - 7*x^6 - x^7 + x^2*O(x^n))); polcoeff(A, n)}
for(n=0, 25, print1(a(n) , ", "))

Crossrefs

Cf. A249926, A249927, A249928, A249929, A249930, A249931.

Sequence in context: A033713 A067422 A347855 * A278751 A145240 A113564

Adjacent sequences: A249929 A249930 A249931 * A249933 A249934 A249935

Keyword

nonn

Author

Paul D. Hanna, Nov 27 2014

Status

approved