|
|
A277362
|
|
Self-convolution of a(n)/4^n gives factorials (A000142).
|
|
2
|
|
|
1, 2, 14, 164, 2646, 53852, 1316364, 37467080, 1215510118, 44249471916, 1785942489700, 79150848980216, 3821494523507708, 199668288426274968, 11225643465179779544, 675769562728962818448, 43370783734391689628294, 2956329387192674856638668
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Self-convolution of a(n) gives A047053.
|
|
LINKS
|
|
|
FORMULA
|
Sum_{k=0..n} a(k)/4^k * a(n-k)/4^(n-k) = n!.
|
|
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:
|
|
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
|
|
|
STATUS
|
approved
|
|
|
|