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A024189
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a(n) = ((n+3)!/2)*Sum_{k=1..n} (-1)^(k+1)/(k+3).
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1
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3, 3, 78, 186, 4008, 15912, 340560, 1931760, 43139520, 321312960, 7611891840, 70589232000, 1783264896000, 19854108288000, 535217663232000, 6967948748544000, 200181525175296000, 2987361024592896000, 91267413626898432000, 1537150149529860096000, 49817611958159130624000
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = ((n+3)!/12)*(5 - 6*log(2) + 3*(-1)^n*(psi((n+4)/2) - psi((n+5)/2))), psi(x) is the digamma function. - G. C. Greubel, Jan 02 2020
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MAPLE
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seq( (n+3)!*(5 + 6*add((-1)^k/k, k=1..n+3))/12, n=1..25); # G. C. Greubel, Jan 02 2020
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MATHEMATICA
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Table[(n+3)!*(5 + 6*Sum[(-1)^k/k, {k, n+3}])/12, {n, 25}] (* G. C. Greubel, Jan 02 2020 *)
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PROG
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(PARI) a(n) = (n+3)!/2*sum(x=1, n, (-1)^(x+1)/(x+3)) \\ Michel Marcus, Mar 21 2013
(Magma) [Factorial(n+3)*(5 + 6*(&+[(-1)^k/k: k in [1..n+3]]))/12: n in [1..25]]; // G. C. Greubel, Jan 02 2020
(Sage) [factorial(n+3)*(5 + 6*sum((-1)^k/k for k in (1..n+3)))/12 for n in (1..25)] # G. C. Greubel, Jan 02 2020
(GAP) List([1..25], n-> Factorial(n+3)*(5 + 6*Sum([1..n+3], k-> (-1)^k/k))/12 ); # G. C. Greubel, Jan 02 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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