A387743 a(n) = (1/5) * Sum_{k=0..n-1} binomial(5*n,5*k+1).

0, 1, 44, 1277, 42317, 1338030, 42995667, 1373879453, 43986122004, 1407312147649, 45036692025545, 1441144164752414, 46116945756093311, 1475738576890744233, 47223675353334490428, 1511157157798262027285, 48357034079030073878613, 1547425034751111343388782

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (21,353,-32).

Formula

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

G.f.: x * (1+23*x)/((1-32*x) * (1+11*x-x^2)).

a(n) = 21*a(n-1) + 353*a(n-2) - 32*a(n-3) for n > 2.

Mathematica

Table[(1/5)*Sum[Binomial[5*n, 5*k+1], {k, 0, n-1}], {n, 0, 18}] (* Vincenzo Librandi, Sep 09 2025 *)

Prog

(PARI) a(n) = sum(k=0, n-1, binomial(5*n, 5*k+1))/5;
(Magma) [&+[(1/5)* Binomial(5*n, 5*k+1): k in [0..n]]: n in [0..15]]; // Vincenzo Librandi, Sep 09 2025

Crossrefs

Cf. A015565, A387745, A387748, A387751, A387752, A387753, A387754.

Cf. A070782, A387744.

Sequence in context: A004340 A387015 A394272 * A231262 A223049 A278793

Adjacent sequences: A387740 A387741 A387742 * A387744 A387745 A387746

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 06 2025

Status

approved