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A107713
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Convolution of 2^n*n! and n!.
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6
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1, 3, 12, 66, 484, 4536, 52128, 709776, 11153376, 198339840, 3932962560, 85976743680, 2053285148160, 53173906652160, 1483987541299200, 44396218792396800, 1417294759310438400, 48088097391133900800, 1728013936221838540800, 65558270633421791232000
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OFFSET
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0,2
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COMMENTS
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E.g.f. is int( 1/((1-t)(1-2*(x+t))), t=0..x).
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} 2^k * k! * (n-k)!.
E.g.f. (for offset 1): (log(1-x)+log(1-2*x))/(-3+2*x).
a(n) ~ n! * 2^n * (1 + 1/(2*n) + 1/(2*n^2) + 5/(4*n^3) + 17/(4*n^4) + 37/(2*n^5) + 98/n^6 + 4885/(8*n^7) + 34969/(8*n^8) + 70657/(2*n^9) + 636151/(2*n^10) + ...). - Vaclav Kotesovec, Aug 08 2019, extended Dec 07 2020
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EXAMPLE
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a(4) = 484 = 4! 0! + 2 3! 1! + 2^2 2! 2! + 2^3 1! 3! + 2^4 0! 4!
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MAPLE
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f:=proc(n) local k; add(2^k*k!*(n-k)!, k=0..n); end:
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MATHEMATICA
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Rest[Range[0, 20]! CoefficientList[Series[((Log[1 - x] + Log[1 - 2 x]))/(-3 + 2 x), {x, 0, 20}], x]] (* Vincenzo Librandi, Jul 13 2015 *)
Table[Sum[2^k * k! * (n-k)!, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Aug 08 2019 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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