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%I #14 Dec 07 2020 17:26:32
%S 1,5,38,430,6640,130200,3088560,85828080,2731899456,97956720000,
%T 3906077932800,171436911264000,8211994618982400,426284974571904000,
%U 23836815193556736000,1428394963614554880000,91316330157374106624000
%N Convolution of 4^n*n! and n!.
%H G. C. Greubel, <a href="/A110467/b110467.txt">Table of n, a(n) for n = 0..360</a>
%F E.g.f. (for offset 1): log((1-x)*(1-4*x))/(4*x-5).
%F a(n) = n!*Sum_{k=0..n} 4^k/binomial(n, k).
%F a(n) = Sum_{k=0..n} k!*4^k*(n-k)!.
%F a(n) ~ 4^n * n! * (1 + 1/(4*n) + 1/(8*n^2) + 7/(32*n^3) + 1/(2*n^4) + 187/(128*n^5) + 1337/(256*n^6) + 22559/(1024*n^7) + 109517/(1024*n^8) + 1202047/(2048*n^9) + 14710847/(4096*n^10) + ...). - _Vaclav Kotesovec_, Dec 07 2020
%t Table[Sum[k!*4^k*(n - k)!, {k, 0, n}], {n, 0, 50}] (* _G. C. Greubel_, Aug 28 2017 *)
%o (PARI) for(n=0,50, print1(sum(k=0,n, k!*4^k*(n-k)!), ", ")) \\ _G. C. Greubel_, Aug 28 2017
%Y Cf. A107713, A108953.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Jul 21 2005
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