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A390237

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

1, 3, 13, 71, 445, 3040, 21998, 165801, 1287993, 10240870, 82939364, 681829854, 5674948844, 47726973679, 404963281675, 3462485634943, 29802561951657, 258025475286759, 2245560767095261, 19633470022380120, 172374674900586262, 1519071406103018848

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

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

FORMULA

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

MATHEMATICA

Table[Sum[(k+1)*(2*k+1)*Binomial[4*n-2*k+1, n-k]/(4*n-2*k+1), {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Dec 03 2025 *)

PROG

(PARI) a(n) = sum(k=0, n, (k+1)*(2*k+1)*binomial(4*n-2*k+1, n-k)/(4*n-2*k+1));

(Magma) [&+[(k+1)*(2*k+1)*Binomial(4*n-2*k+1, n-k)/(4*n-2*k+1): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Dec 03 2025

CROSSREFS

Cf. A002293, A390709, A391198.

Sequence in context: A198447 A318223 A162326 * A122455 A126390 A272428

Adjacent sequences: A390234 A390235 A390236 * A390238 A390239 A390240

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Dec 02 2025

STATUS

approved

URL: https://oeis.org/A390237

⇱ A390237 - OEIS