A366025 Expansion of (1/x) * Series_Reversion( x*(1-x)/(1+x^5) ).

1, 1, 2, 5, 14, 43, 139, 465, 1595, 5577, 19804, 71228, 258946, 950030, 3513050, 13079920, 48993149, 184490361, 698020080, 2652192675, 10115878915, 38717526745, 148655862210, 572412768275, 2209969761924, 8553073927858, 33176952295730, 128960722306128

Offset

0,3

Links

Table of n, a(n) for n=0..27.

Formula

G.f. satisfies A(x) = 1 + x*A(x)^2*(1 + x^4*A(x)^3).

a(n) = Sum_{k=0..floor(n/5)} binomial(n-4*k,k) * binomial(2*n-5*k+1,n-4*k)/(2*n-5*k+1) = (1/(n+1)) * Sum_{k=0..floor(n/5)} binomial(n+1,k) * binomial(2*n-5*k,n-5*k).

Mathematica

CoefficientList[InverseSeries[Series[x(1-x)/(1+x^5), {x, 0, 28}], x]/x, x] (* Stefano Spezia, Sep 26 2023 *)

Prog

(PARI) a(n) = sum(k=0, n\5, binomial(n-4*k, k)*binomial(2*n-5*k+1, n-4*k)/(2*n-5*k+1));
(PARI) Vec(serreverse(x*(1-x)/(1+x^5)+O(x^30))/x) \\ Michel Marcus, Sep 26 2023

Crossrefs

Cf. A006318, A052709, A071969, A365268.

Cf. A365760, A366024.

Sequence in context: A052301 A071755 A149879 * A366042 A149880 A066351

Adjacent sequences: A366022 A366023 A366024 * A366026 A366027 A366028

Keyword

nonn

Author

Seiichi Manyama, Sep 26 2023

Status

approved