A391542 a(n) = Sum_{k=0..n} binomial(4*n+k,n).

1, 9, 109, 1325, 15981, 191470, 2283471, 27152235, 322294765, 3822163565, 45314215530, 537292624687, 6373294023279, 75644665941720, 898481199871384, 10680451886046855, 127068624623021805, 1513080648154295439, 18032665691533735935, 215092576922893063356, 2567723878202478453370

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..900

Formula

a(n) = binomial(5*n+1,n+1) - binomial(4*n,n+1).

Mathematica

Table[Sum[Binomial[4*n+k, n], {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Dec 20 2025 *)

Prog

(PARI) a(n) = binomial(5*n+1, n+1)-binomial(4*n, n+1);
(Magma) [&+[Binomial(4*n+k, n): k in [0..n]] : n in [0..25] ]; // Vincenzo Librandi, Dec 20 2025

Crossrefs

Cf. A108079, A387117.

Sequence in context: A267795 A128876 A199030 * A288692 A358601 A388913

Adjacent sequences: A391539 A391540 A391541 * A391543 A391544 A391545

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 13 2025

Status

approved