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URL: https://oeis.org/A277362

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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
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!.
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
STATUS
approved