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A091032
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Second column (k=3) of array A090438 ((4,2)-Stirling2) divided by 8.
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2
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1, 60, 5040, 604800, 99792000, 21794572800, 6102480384000, 2134124568576000, 912338253066240000, 468333636574003200000, 284372184127734743040000, 201645730563302817792000000, 165147853331345007771648000000
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OFFSET
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2,2
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LINKS
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FORMULA
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a(n) = A090438(n, 3)/8 = (n-1)*(2*n)!/4!
E.g.f.: (-3*hypergeom([1/2, 1], [], 4*x) + hypergeom([1, 3/2], [], 4*x) + 2)/(8*3!) (cf. A090438).
Sum_{n>=2} 1/a(n) = 60 - 24*Gamma - 24*cosh(1) + 24*CoshIntegral(1) - 24*sinh(1).
Sum_{n>=2} (-1)^n/a(n) = -12 + 24*gamma - 24*cos(1) - 24*CosIntegral(1) + 24*SinIntegral(1). (End)
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MATHEMATICA
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a[n_] := (n - 1)*(2*n)!/4!; Array[a, 13, 2] (* Amiram Eldar, Nov 03 2022 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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