A387754 a(n) = (1/11) * Sum_{k=0..n-1} binomial(11*n,11*k+1).

0, 1, 58788, 40670763, 185108030865, 246239904868235, 676789916853575024, 1161855874385326807002, 2670834866840604221483210, 5091238698394031792492322609, 10918901752862768011376203844356, 21722478184802243536051721464074561, 45318603598378626175486293712156106912

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Index entries for linear recurrences with constant coefficients, signature (1035,2452907,-767040961,-15735018638,2061791231,2048).

Formula

a(n) = (1/11) * Sum_{k=0..n-1} binomial(11*n,11*k+10).

G.f.: x * (1+57753*x-22627724*x^2-420664595*x^3+32698825*x^4)/((1-2048*x) * (1+1013*x-378283*x^2-7682623*x^3+1006734*x^4+x^5)).

a(n) = 1035*a(n-1) + 2452907*a(n-2) - 767040961*a(n-3) - 15735018638*a(n-4) + 2061791231*a(n-5) + 2048*a(n-6) for n > 5.

Mathematica

Table[(1/11)*Sum[Binomial[11*n, 11*k+1], {k, 0, n-1}], {n, 0, 12}] (* Vincenzo Librandi, Sep 07 2025 *)
LinearRecurrence[{1035, 2452907, -767040961, -15735018638, 2061791231, 2048}, {0, 1, 58788, 40670763, 185108030865, 246239904868235}, 20] (* Harvey P. Dale, Dec 31 2025 *)

Prog

(PARI) a(n) = sum(k=0, n-1, binomial(11*n, 11*k+1))/11;
(Magma) [&+[(1/11)* Binomial(11*n, 11*k+1): k in [0..n]]: n in [0..15]]; // Vincenzo Librandi, Sep 07 2025

Crossrefs

Cf. A015565, A387743, A387745, A387748, A387751, A387752, A387753.

Sequence in context: A234447 A227601 A147700 * A214118 A157131 A217603

Adjacent sequences: A387751 A387752 A387753 * A387755 A387756 A387757

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 06 2025

Status

approved