A387850 a(n) = Sum_{k=0..n} binomial(5*n,6*k).

1, 1, 211, 5461, 164921, 5858126, 174174002, 5791193143, 182670807229, 5864062014805, 187791199242011, 6000986704418168, 192222214478506046, 6147988181142091285, 196773608710418383855, 6296488643826193618261, 201485610324861686296229, 6447659080772588021279210

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Index entries for linear recurrences with constant coefficients, signature (6,615,7160,-7155,7776).

Formula

G.f.: (1-5*x-410*x^2-3580*x^3+2385*x^4-1296*x^5)/((1-32*x) * (1-x+x^2) * (1+27*x+243*x^2)).

a(n) = 6*a(n-1) + 615*a(n-2) + 7160*a(n-3) - 7155*a(n-4) + 7776*a(n-5) for n > 5.

Mathematica

Table[Sum[ Binomial[ 5*n, 6*k], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Sep 13 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(5*n, 6*k));
(Magma) [&+[Binomial(5*n, 6*k): k in [0..n]]: n in [0..40]]; // Vincenzo Librandi, Sep 13 2025

Crossrefs

Cf. A070967, A306847, A377627, A378031, A387849.

Sequence in context: A185719 A224101 A013529 * A229519 A289983 A212851

Adjacent sequences: A387847 A387848 A387849 * A387851 A387852 A387853

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 10 2025

Status

approved