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
KEYWORD
nonn
AUTHOR
Ralf Stephan, Sep 23 2004
STATUS
approved