A099021 Main diagonal of array in A099020.

1, 1, 4, 24, 198, 2070, 26160, 387240, 6565020, 125341020, 2659925520, 62089917120, 1580632348680, 43571319671880, 1292731109429760, 41068078953501600, 1390717740470058000, 50003952605673066000, 1902359109096675028800, 76341746199227491382400

Offset: 0

Author

Ralf Stephan, Sep 23 2004

Keywords

• nonn

Comments

Diagonal of Euler-Seidel matrix with start sequence A001147.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..150

Programs

Maple

a:= proc(n) a(n):= `if`(n<3, [1, 1, 4][n+1],
      (4*n-3)*a(n-1) -(n-1)*(4*n-7)*a(n-2) -(n-2)*(n-1)*a(n-3))
    end:
seq (a(n), n=0..20);  # Alois P. Heinz, Oct 20 2012

Mathematica

Table[n!*SeriesCoefficient[E^(x^2/(2-4*x))/Sqrt[1-2*x],{x,0,n}],{n,0,20}] (* Vaclav Kotesovec, Oct 14 2012 *)

Formula

a(n) = (1/(sqrt(2*Pi)))*Int(exp(-x^2/2)*(x(1+x))^n,x,-infinity,infinity). - Paul Barry, Apr 19 2010

Contribution from Vaclav Kotesovec, Oct 14 2012: (Start)

E.g.f.: exp(x^2/(2-4*x))/sqrt(1-2*x).

Recurrence: a(n) = (4*n-3)*a(n-1) - (n-1)*(4*n-7)*a(n-2) - (n-2)*(n-1)*a(n-3).

a(n) ~ 2^(n-1/2)*exp(sqrt(n/2)-n-3/16)*n^n.

(End)