OFFSET
0,2
COMMENTS
Self-convolution of a(n) gives A047053.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..360
FORMULA
Sum_{k=0..n} a(k)/4^k * a(n-k)/4^(n-k) = n!.
a(n) ~ 2^(2*n-1) * n!. - Vaclav Kotesovec, Oct 27 2021
MAPLE
a:= proc(n) option remember; `if`(n=0, 1,
(n!*4^n-add(a(k)*a(n-k), k=1..n-1))/2)
end:
seq(a(n), n=0...20); # Alois P. Heinz, Oct 12 2016
MATHEMATICA
With[{n = 20}, Sqrt[Sum[k! (4 x)^k, {k, 0, n - 1}] + O[x]^n][[3]]]
CoefficientList[Series[Sqrt[-Gamma[0, -1/(4*x)]/(x*E^(1/(4*x)))]/2, {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 27 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Reshetnikov, Oct 10 2016
STATUS
approved