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%I #14 Oct 27 2021 13:35:29
%S 1,2,14,164,2646,53852,1316364,37467080,1215510118,44249471916,
%T 1785942489700,79150848980216,3821494523507708,199668288426274968,
%U 11225643465179779544,675769562728962818448,43370783734391689628294,2956329387192674856638668
%N Self-convolution of a(n)/4^n gives factorials (A000142).
%C Self-convolution of a(n) gives A047053.
%H Vaclav Kotesovec, <a href="/A277362/b277362.txt">Table of n, a(n) for n = 0..360</a>
%F Sum_{k=0..n} a(k)/4^k * a(n-k)/4^(n-k) = n!.
%F a(n) ~ 2^(2*n-1) * n!. - _Vaclav Kotesovec_, Oct 27 2021
%p a:= proc(n) option remember; `if`(n=0, 1,
%p (n!*4^n-add(a(k)*a(n-k), k=1..n-1))/2)
%p end:
%p seq(a(n), n=0...20); # _Alois P. Heinz_, Oct 12 2016
%t With[{n = 20}, Sqrt[Sum[k! (4 x)^k, {k, 0, n - 1}] + O[x]^n][[3]]]
%t CoefficientList[Series[Sqrt[-Gamma[0, -1/(4*x)]/(x*E^(1/(4*x)))]/2, {x, 0, 20}], x] (* _Vaclav Kotesovec_, Oct 27 2021 *)
%Y Cf. A000142, A000302, A047053.
%K nonn
%O 0,2
%A _Vladimir Reshetnikov_, Oct 10 2016
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