A387906 a(n) = Sum_{k=0..n} binomial(4*n+3,5*k).

1, 22, 474, 6008, 107883, 1669801, 26789257, 430470899, 6863694378, 109996928003, 1759098789526, 28146676447417, 450374698997499, 7205634556190798, 115292842751246298, 1844672594930734801, 29514778095285204502, 472236871202375365274, 7555784484021765207768

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..830

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

Formula

G.f.: (1+17*x+234*x^2+38*x^3+8*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+3, 5*k], {k, 0, n}], {n, 0, 30}] (* Vincenzo Librandi, Oct 15 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(4*n+3, 5*k));
(Magma) [&+[Binomial(4*n+3, 5*k) : k in [0..n] ]: n in [0..40]]; // Vincenzo Librandi, Oct 15 2025

Crossrefs

Cf. A387873, A387905.

Sequence in context: A276644 A139228 A240782 * A261135 A158535 A171327

Adjacent sequences: A387903 A387904 A387905 * A387907 A387908 A387909

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 12 2025

Status

approved