A390472 a(n) = Sum_{k=0..n} binomial(4*n-2*k+2,n-k).

1, 7, 54, 441, 3724, 32130, 281359, 2490695, 22231341, 199723668, 1803710336, 16359723198, 148919995615, 1359760296769, 12448518709446, 114227100633785, 1050254412280420, 9673701429423411, 89244021409649401, 824484497216920684, 7626792613840800615

Offset

0,2

Links

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

Formula

G.f.: g^2/((1-4*x*g^3) * (1-x*g^2)) where g = 1+x*g^4 is the g.f. of A002293.

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

a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(4*n-k+3,n-2*k).

Mathematica

Table[Sum[Binomial[4*n-2*k+2, n-k], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Nov 07 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(4*n-2*k+2, n-k));
(Magma) [&+[Binomial(4*n-2*k+2, n-k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 08 2025

Crossrefs

Cf. A224274, A387009, A389471, A390335, A390471, A390473, A390474.

Cf. A371786, A390407, A390413.

Cf. A002293.

Sequence in context: A015562 A243670 A388412 * A152108 A093742 A291703

Adjacent sequences: A390469 A390470 A390471 * A390473 A390474 A390475

Keyword

nonn

Author

Seiichi Manyama, Nov 06 2025

Status

approved