A387751 a(n) = (1/8) * Sum_{k=0..n-1} binomial(8*n,8*k+1).

0, 1, 1432, 206704, 74642176, 16156225792, 4537141479424, 1106999369445376, 290798623718244352, 73437997034388127744, 18936886018938727038976, 4829259730232104019034112, 1238815603122773037011697664, 316793676471943557329742462976, 81145804813160759265638137987072

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (120,34800,4096).

Formula

a(n) = (1/8) * Sum_{k=0..n-1} binomial(8*n,8*k+7).

G.f.: x * (1+1312*x+64*x^2)/((1-256*x) * (1+136*x+16*x^2)).

a(n) = 120*a(n-1) + 34800*a(n-2) + 4096*a(n-3) for n > 3.

E.g.f.: (cosh(256*x) + sinh(256*x) - 2*sqrt(2)*exp(-68*x)*sinh(48*sqrt(2)*x) - 1)/64. - Stefano Spezia, Sep 07 2025

Mathematica

Table[(1/8)*Sum[Binomial[8*n, 8*k+1], {k, 0, n-1}], {n, 0, 14}] (* Vincenzo Librandi, Sep 08 2025 *)

Prog

(PARI) a(n) = sum(k=0, n-1, binomial(8*n, 8*k+1))/8;
(Magma) [&+[(1/8)* Binomial(8*n, 8*k+1): k in [0..n]]: n in [0..15]]; // Vincenzo Librandi, Sep 08 2025

Crossrefs

Cf. A015565, A387743, A387745, A387748, A387752, A387753, A387754.

Cf. A070832.

Sequence in context: A208628 A205070 A169822 * A114083 A143475 A245948

Adjacent sequences: A387748 A387749 A387750 * A387752 A387753 A387754

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 06 2025

Status

approved