A387873 a(n) = Sum_{k=0..n} binomial(4*n+1,5*k).

1, 2, 127, 1574, 25773, 427351, 6643782, 107746282, 1717012749, 27481113638, 439924466026, 7035859329512, 112595619434887, 1801425114687749, 28822936611339453, 461170414282959151, 7378682274243863442, 118059247217851456567, 1888946370232447241574

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

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

Formula

G.f.: (1-3*x-13*x^2-61*x^3-22*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+1, 5*k], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Sep 14 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(4*n+1, 5*k));
(Magma) [&+[Binomial(4*n+1, 5*k): k in [0..n]]: n in [0..20]]; // Vincenzo Librandi, Sep 14 2025

Crossrefs

Cf. A387848.

Sequence in context: A141928 A343184 A062588 * A125634 A075596 A092832

Adjacent sequences: A387870 A387871 A387872 * A387874 A387875 A387876

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 10 2025

Status

approved