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A051431
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a(n) = (n+10)!/10!.
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12
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1, 11, 132, 1716, 24024, 360360, 5765760, 98017920, 1764322560, 33522128640, 670442572800, 14079294028800, 309744468633600, 7124122778572800, 170978946685747200, 4274473667143680000, 111136315345735680000, 3000680514334863360000, 84019054401376174080000
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OFFSET
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0,2
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COMMENTS
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The p=10 member of the p-family of sequences {(n+p-1)!/p!}, n >= 1.
The asymptotic expansion of the higher-order exponential integral E(x,m=1,n=11) ~ exp(-x)/x*(1 - 11/x + 132/x^2 - 1716/x^3 + 24024/x^4 - 360360/x^5 + 5765760/x^6 - ...) leads to the sequence given above. See A163931 and A130534 for more information. - Johannes W. Meijer, Oct 20 2009
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LINKS
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FORMULA
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a(n) = (n+10)!/10!
E.g.f.: 1/(1-x)^11.
Sum_{n>=0} 1/a(n) = 3628800*e - 9864100.
Sum_{n>=0} (-1)^n/a(n) = 3628800/e - 1334960. (End)
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MATHEMATICA
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a[n_] := (n + 10)!/10!; Array[a, 20, 0] (* Amiram Eldar, Jan 15 2023 *)
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PROG
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(Haskell)
a051431 = (flip div 3628800) . a000142 . (+ 10)
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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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