A249931 G.f. A(x) satisfies: 1+x = A(x)^3 + A(x)^5 - A(x)^7.

1, 1, 8, 152, 3550, 92788, 2597399, 76156625, 2308825896, 71786597460, 2276556265566, 73352261863414, 2394513305129959, 79024386863955715, 2632253500369515600, 88379408361414983552, 2987975394537672941171, 101633132452812322479087, 3475524159518622818586778

Offset

0,3

Links

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

Formula

G.f.: 1 + Series_Reversion(x - 8*x^2 - 24*x^3 - 30*x^4 - 20*x^5 - 7*x^6 - x^7).

Example

 G.f.: A(x) = 1 + x + 8*x^2 + 152*x^3 + 3550*x^4 + 92788*x^5 +...
Related expansions.
A(x)^3 = 1 + 3*x + 27*x^2 + 505*x^3 + 11778*x^4 + 307608*x^5 +...
A(x)^5 = 1 + 5*x + 50*x^2 + 930*x^3 + 21675*x^4 + 565901*x^5 +...
A(x)^7 = 1 + 7*x + 77*x^2 + 1435*x^3 + 33453*x^4 + 873509*x^5 +...
where 1+x = A(x)^3 + A(x)^5 - A(x)^7.

Prog

 (PARI) /* From 1+x = A(x)^3 + A(x)^5 - A(x)^7: */
{a(n)=local(A=[1, 1]); for(i=1, n, A=concat(A, 0); A[#A]=-Vec(Ser(A)^3+Ser(A)^5-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 - 8*x^2 - 24*x^3 - 30*x^4 - 20*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, A249932.

Sequence in context: A053606 A367701 A221732 * A123770 A003400 A360338

Adjacent sequences: A249928 A249929 A249930 * A249932 A249933 A249934

Keyword

nonn

Author

Paul D. Hanna, Nov 27 2014

Status

approved