A387848 a(n) = Sum_{k=0..n} binomial(4*n,5*k).

1, 1, 57, 859, 12393, 215766, 3321891, 53774932, 859595529, 13733091643, 219993856006, 3517929664756, 56296324109907, 900729032983924, 14411355379952868, 230585685502492596, 3689341137121931721, 59029601136140621857, 944473434343229560419, 15111570273013075344193

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..831

Index entries for linear recurrences with constant coefficients, signature (5,130,740,-65,16).

Formula

G.f.: (1-4*x-78*x^2-296*x^3+13*x^4)/((1-16*x) * (1+11*x+46*x^2-4*x^3+x^4)).

a(n) = 5*a(n-1) + 130*a(n-2) + 740*a(n-3) - 65*a(n-4) + 16*a(n-5) for n > 4.

Mathematica

Table[Sum[Binomial[4*n, 5*k], {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Sep 15 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(4*n, 5*k));
(Magma) [&+[Binomial(4*n, 5*k): k in [0..n]]: n in [0..25]]; // Vincenzo Librandi, Sep 15 2025

Crossrefs

Cf. A070782, A139398, A387844, A387847.

Cf. A070775, A387849.

Sequence in context: A210149 A254783 A233370 * A008390 A231311 A008922

Adjacent sequences: A387845 A387846 A387847 * A387849 A387850 A387851

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 10 2025

Status

approved