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

0,3

Comments

Diagonal of Euler-Seidel matrix with start sequence A001147.

Links

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

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)

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 *)

Crossrefs

Sequence in context: A101370 A201338 A362355 * A220690 A136229 A138419

Adjacent sequences: A099018 A099019 A099020 * A099022 A099023 A099024

Keyword

nonn

Author

Ralf Stephan, Sep 23 2004

Status

approved