A360602 a(n) = ((2*n + 1)! / n!)^2 / (n + 1).

1, 18, 1200, 176400, 45722880, 18441561600, 10685567692800, 8414884558080000, 8646761377013760000, 11237331085567082496000, 18020592759036666839040000, 34953943088278121445457920000, 80662945588334126412595200000000, 218412210097326433146332774400000000

Offset: 0

Author

Peter Luschny, Feb 16 2023

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Modified Struve Function.
• Eric Weisstein's World of Mathematics, Struve function.
• Wikipedia, Struve function.

Crossrefs

Cf. A122747, A000108, A000407.

Programs

Maple

a := n -> ((2*n + 1)! / n!)^2 / (n + 1):
seq(a(n), n = 0..13);

Mathematica

a[n_] := ((2*n + 1)!/n!)^2/(n + 1); Array[a, 14, 0] (* Amiram Eldar, Mar 02 2023 *)

Formula

a(n) = CatalanNumber(n) * (2*n)! * (2*n + 1)^2.

a(n) ~ (4*n/e)^(2*n)*(8*n - 2/3).

From Amiram Eldar, Mar 02 2023: (Start)

Sum_{n>=0} 1/a(n) = 1/2 + StruveL(0, 1/2)*Pi/2 + StruveL(1, 1/2)*Pi/4, where StruveL is the modified Struve function.

Sum_{n>=0} (-1)^n/a(n) = 1/2 + StruveH(0, 1/2)*Pi/2 - StruveH(1, 1/2)*Pi/4, where StruveH is the Struve function. (End)