A390720 a(n) = Sum_{k=0..n} (k+2) * binomial(4*n-3*k+2,n-k)/(4*n-3*k+2).

1, 3, 13, 72, 459, 3183, 23315, 177449, 1389355, 11117962, 90523311, 747511830, 6245348236, 52696347125, 448402255002, 3843467085879, 33154739732284, 287611257523989, 2507438148639917, 21957792012871833, 193057223885954300, 1703552048286899566, 15081783511111280527, 133922291015426876111

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

G.f.: g^2/(1-x*g) where g = 1+x*g^4 is the g.f. of A002293.

Mathematica

Table[Sum[(k+2)*Binomial[4*n-3*k+2, n-k]/(4*n-3*k+2), {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Nov 17 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (k+2)*binomial(4*n-3*k+2, n-k)/(4*n-3*k+2));
(Magma) [&+[(k+2)*Binomial(4*n-3*k+2, n-k)/(4*n-3*k+2): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 17 2025

Crossrefs

Cf. A000245, A390719, A390721.

Cf. A002293.

Sequence in context: A188051 A247230 A047159 * A383563 A086662 A293195

Adjacent sequences: A390717 A390718 A390719 * A390721 A390722 A390723

Keyword

nonn

Author

Seiichi Manyama, Nov 16 2025

Status

approved