A387755 a(n) = (1/4) * Sum_{k=0..n-1} binomial(10*n,10*k+5).

0, 63, 7752, 38850633, 20113001532, 32728067456378, 25984316034491262, 31274811079670383673, 29132020107222475528192, 31624956307158955774498143, 31271890443423600645864024822, 32711850575007686745867477968538, 33069513438169059586030270086668652

Offset

0,2

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

G.f.: x * (63-25134*x-2227122*x^2+9888000*x^3+80000*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[(1/4)*Sum[Binomial[10*n, 10*k+5], {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+5))/4;
(Magma) [&+[(1/4)* Binomial(10*n, 10*k+5): k in [0..n]]: n in [0..15]]; // Vincenzo Librandi, Sep 08 2025

Crossrefs

Cf. A070833, A387753.

Sequence in context: A093263 A069433 A178634 * A174763 A160871 A183525

Adjacent sequences: A387752 A387753 A387754 * A387756 A387757 A387758

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 06 2025

Status

approved