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A294193
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a(n) = sum of integers between n!+1 and (n+1)!.
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3
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0, 2, 18, 279, 6960, 252300, 12443760, 800168040, 65028257280, 6518255405760, 790091384544000, 113924591159702400, 19273172758289049600, 3780639334294658035200, 851206099134433961318400, 218026562222345234117760000, 63037891684425054948655104000
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OFFSET
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0,2
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COMMENTS
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Useful as a growth reference for sequences summing on intervals between 2 factorials.
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LINKS
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FORMULA
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a(n) = 1/2 * ((n + 1)!*((n + 1)! + 1) - n!*(n! + 1) ).
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EXAMPLE
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a(2) = 3 + 4 + 5 + 6 = 18.
a(3) = 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24 = 24*25/2 - 6*7/2 = 279.
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MATHEMATICA
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Table[1/2 ((n + 1)! ((n + 1)! + 1) - n! (n! + 1) ), {n, 0, 10}]
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PROG
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(PARI) a(n) = 1/2*((n+1)!*((n+1)! + 1)-n!*(n!+1)) \\ Iain Fox, Nov 28 2017
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CROSSREFS
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Cf. A001563 (difference of factorials).
Cf. A049775 (same idea between consecutive powers of 2).
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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