A387753 a(n) = (1/10) * Sum_{k=0..n-1} binomial(10*n,10*k+1).

0, 1, 16798, 6893448, 13386764876, 9777324861855, 12447922046933484, 11236371108841435107, 12442354958165416418872, 12160494995305079344036204, 12812218479151457046818046790, 12896605931447181698327428012521, 13344440991130769390803039024140488

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..250

Index entries for linear recurrences with constant coefficients, signature (522,587797,-75135226,-392963125,3200000).

Formula

a(n) = (1/10) * Sum_{k=0..n-1} binomial(10*n,10*k+9).

G.f.: x * (1+16276*x-2462905*x^2-10293760*x^3+32000*x^4)/((1-1024*x) * (1-123*x+x^2) * (1+625*x+3125*x^2)).

a(n) = 522*a(n-1) + 587797*a(n-2) - 75135226*a(n-3) - 392963125*a(n-4) + 3200000*a(n-5) for n > 5.

Mathematica

Table[(1/10)*Sum[Binomial[10*n, 10*k+1], {k, 0, n-1}], {n, 0, 14}] (* Vincenzo Librandi, Sep 08 2025 *)

Prog

(PARI) a(n) = sum(k=0, n-1, binomial(10*n, 10*k+1))/10;
(Magma) [&+[(1/10)* Binomial(10*n, 10*k+1): k in [0..n]]: n in [0..15]]; // Vincenzo Librandi, Sep 08 2025

Crossrefs

Cf. A015565, A387743, A387745, A387748, A387751, A387752, A387754.

Cf. A070833, A387755.

Sequence in context: A227600 A147698 A208630 * A067493 A016925 A265472

Adjacent sequences: A387750 A387751 A387752 * A387754 A387755 A387756

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 06 2025

Status

approved