OFFSET
0,5
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Robert Israel, Linear recurrence of order 20
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+1,k) * binomial(4*k,n-3*k).
a(n) = (1/(n+1)) * [x^n] (1 + x^3 * (1 + x)^4)^(n+1).
D-finite with recurrence of order 20 (see link). - Robert Israel, Apr 07 2026
MATHEMATICA
Table[(1/(n+1)) Coefficient[((1+x^3*(1+x)^4))^(n+1), x, n], {n, 0, 31}] (* Vincenzo Librandi, Sep 28 2025 *)
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(serreverse(x/(1+x^3*(1+x)^4))/x)
(Magma) R<x> := PolynomialRing(Rationals()); [ (1/(n+1))*Coefficient(((1 + x^3 * (1 + x)^4))^(n+1), n) : n in [0..30] ]; // Vincenzo Librandi, Sep 28 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 25 2025
STATUS
approved
