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A110467
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Convolution of 4^n*n! and n!.
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4
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1, 5, 38, 430, 6640, 130200, 3088560, 85828080, 2731899456, 97956720000, 3906077932800, 171436911264000, 8211994618982400, 426284974571904000, 23836815193556736000, 1428394963614554880000, 91316330157374106624000
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OFFSET
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0,2
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LINKS
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FORMULA
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E.g.f. (for offset 1): log((1-x)*(1-4*x))/(4*x-5).
a(n) = n!*Sum_{k=0..n} 4^k/binomial(n, k).
a(n) = Sum_{k=0..n} k!*4^k*(n-k)!.
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
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MATHEMATICA
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Table[Sum[k!*4^k*(n - k)!, {k, 0, n}], {n, 0, 50}] (* G. C. Greubel, Aug 28 2017 *)
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PROG
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(PARI) for(n=0, 50, print1(sum(k=0, n, k!*4^k*(n-k)!), ", ")) \\ G. C. Greubel, Aug 28 2017
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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