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A004664 n! + n^2. 4
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; text; internal format)
OFFSET

0,2

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 a perfect square for n>=1 up to n=30,000. - Alexander R. Povolotsky, Sep 26 2008

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for sequences related to factorial numbers

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). - Alexander R. Povolotsky, Nov 06 2010

MATHEMATICA

Table[n! + n^2, {n, 0, 20}] (* Stefan Steinerberger, Apr 11 2006 *)

PROG

(MAGMA) [Factorial(n) + n^2: n in [0..25]]; // Vincenzo Librandi, Jul 26 2013

CROSSREFS

Sequence in context: A316981 A319560 A061322 * A074446 A303551 A180666

Adjacent sequences:  A004661 A004662 A004663 * A004665 A004666 A004667

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

One more term from Stefan Steinerberger, Apr 11 2006

STATUS

approved

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Last modified February 27 03:30 EST 2020. Contains 332299 sequences. (Running on oeis4.)