A307376 a(n) = 1/n! * Sum_{k=0..n} (2*n+k)!/((n-k)!*k!*2^k).

1, 5, 81, 2330, 97405, 5360607, 366432990, 29948982492, 2849278444155, 309333396512855, 37741150862494651, 5112458462852223210, 761358344010536141506, 123636426598733578925150, 21742842987398075489784900, 4116720379411455407932693320, 834934865669512891440715729125

Offset: 0

Author

Seiichi Manyama, Apr 06 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..313

Crossrefs

Cf. A144505.

Programs

Mathematica

Table[Sum[(2*n + k)!/((n - k)!*k!*2^k)/n!, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Apr 06 2019 *)

PARI

{a(n) = sum(k=0, n, (2*n+k)!/((n-k)!*k!*2^k))/n!}

Formula

a(n) = (-1)^n * A144505(2*n+1, n).

a(n) ~ 3^(3*n + 1/2) * n^(n - 1/2) / (sqrt(Pi) * 2^(n + 1/2) * exp(n - 2/3)). - Vaclav Kotesovec, Apr 06 2019