OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(n+1,k) * binomial(8*n-4*k+8,n-k).
a(n) = (1/(n+1)) * [x^n] ((1+x)^4 * (x+(1+x)^4))^(n+1).
MATHEMATICA
Table[(1/(n+1)) Coefficient[((1+x)^4*(x+(1+x)^4))^(n+1), x, n], {n, 0, 19}] (* Vincenzo Librandi, Sep 30 2025 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x/((1+x)^4*(x+(1+x)^4)))/x)
(Magma) R<x> := PolynomialRing(Rationals()); [ (1/(n+1))*Coefficient(((1+x)^4 * (x+(1+x)^4))^(n+1), n) : n in [0..30] ]; // Vincenzo Librandi, Sep 30 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 20 2025
STATUS
approved
