A387905 a(n) = Sum_{k=0..n} binomial(4*n+2,5*k).

1, 7, 254, 3004, 53143, 843756, 13333932, 215492564, 3431847189, 54986385093, 879683351911, 14072420067757, 225191238869774, 3602817278095399, 57646238657975068, 922338323835136341, 14757375158697584607, 236118494435702913134, 3777892242010882603884

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+2*x+89*x^2+84*x^3-12*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+2, 5*k], {k, 0, n}], {n, 0, 30}] (* Vincenzo Librandi, Oct 15 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(4*n+2, 5*k));
(Magma) [&+[Binomial(4*n+2, 5*k) : k in [0..n] ]: n in [0..40]]; // Vincenzo Librandi, Oct 15 2025

Crossrefs

Cf. A387873, A387906.

Sequence in context: A381751 A203474 A366866 * A228291 A119942 A188421

Adjacent sequences: A387902 A387903 A387904 * A387906 A387907 A387908

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 12 2025

Status

approved