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1, 2, 6, 15, 40, 145, 756, 5089, 40384, 362961, 3628900, 39916921, 479001744, 6227020969, 87178291396, 1307674368225, 20922789888256, 355687428096289, 6402373705728324, 121645100408832361, 2432902008176640400
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| It appears (conjectured by me) that n! + n^2 != m^2 for n>=1, m>=0 (n=0 is not included in above conjecture because obviously A004664(0) =1) I checked using PARI that indeed n! +n^2 doesn't yield perfect square for n>=1 up to n=30,000 [From Alexander R.Povolotsky (pevnev(AT)juno.com), Sep 26 2008]
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LINKS
| Index entries for sequences related to factorial numbers
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FORMULA
| Possible recurrence relation (according to WolframAlpha): a(n+2)=((n+2)*(n^3+n^2-n-2)*a(n+1))/(n^3-2*n-1)-((n+2)*(n^2+n-1)*a(n))/(n^2-n-1) [From Alexander R. Povolotsky (pevnev(AT)juno.com), Nov 06 2010]
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MATHEMATICA
| Table[n! + n^2, {n, 0, 20}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 11 2006
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CROSSREFS
| Sequence in context: A062106 A206000 A061322 * A074446 A180666 A121328
Adjacent sequences: A004661 A004662 A004663 * A004665 A004666 A004667
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| One more term from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 11 2006
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