A175925 a(n) = (2*n+1)*(n+1)!.

1, 6, 30, 168, 1080, 7920, 65520, 604800, 6168960, 68947200, 838252800, 11017036800, 155675520000, 2353813862400, 37922556672000, 648606486528000, 11737685127168000, 224083079700480000, 4500868715126784000

Offset: 0

Author

R. J. Mathar, Oct 19 2010

Keywords

• nonn
• easy

Comments

The denominators of the Taylor expansion coefficients of the double integral d(u) = int_0^1 dx int_0^1 dy exp(-u^2*(x-y)^2) = Sum_{n>=0} (-1)^n*u^(2n)/a(n).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..400
• D. H. Bailey, J. M. Borwein, R. E. Crandall, Advances in the theory of box integrals, Math. Comp. 79 (271) (2010) 1839-1866, eq (18).
• Milan Janjić, Pascal Matrices and Restricted Words, J. Int. Seq., Vol. 21 (2018), Article 18.5.2.

Crossrefs

Cf. A000142, A005408, A007680.

Programs

Magma

[(2*n+1)*Factorial(n+1): n in [0..20]]; // Vincenzo Librandi, Oct 11 2011

Maple

A := proc(n) (2*n+1)*(n+1)! ; end proc:

Mathematica

Table[(2n+1)(n+1)!,{n,0,20}] (* Harvey P. Dale, Sep 30 2011 *)

Formula

a(n) = A005408(n)*A000142(n+1) = (n+1)*A007680(n).

E.g.f.: (1 + 3*x)/(1 - x)^3. - Ilya Gutkovskiy, May 12 2017

From Amiram Eldar, Aug 04 2020: (Start)

Sum_{n>=0} 1/a(n) = sqrt(Pi)*erfi(1) + 1 - e.

Sum_{n>=0} (-1)^n/a(n) = sqrt(Pi)*erf(1) - 1 + 1/e. (End)