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A061062
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Sum of squared factorials: (0!)^2 + (1!)^2 + (2!)^2 + (3!)^2 +...+ (n!)^2.
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4
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1, 2, 6, 42, 618, 15018, 533418, 25935018, 1651637418, 133333531818, 13301522971818, 1606652445211818, 231049185247771818, 39006837228880411818, 7639061293780877851818, 1717651314017980301851818
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| There is a Kurepa-like conjecture (see A049782) for this sequence: for primes p>3, p does not divide a(p-1). However, the conjecture fails for p=20879. - T. D. Noe (noe(AT)sspectra.com), Dec 08 2004
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,100
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FORMULA
| Or, a(n) = Sum[(n-k)!^2 {k=0...n}] - Ross La Haye (rlahaye(AT)new.rr.com), Sep 21 2004
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EXAMPLE
| a(2)=0!*0!+1!*1!+2!*2!=6.
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MAPLE
| seq(add((count(Permutation(k)))^2, k=0..n), n=0..15); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 17 2006
a:=n->sum((k!)^2, k=0..n): seq(a(n), n=0..15); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 22 2008
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MATHEMATICA
| s=0; Table[s=s+(n!)^2, {n, 0, 20}]
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PROG
| (PARI) { a=0; for (n=0, 100, write("b061062.txt", n, " ", a+=(n!)^2) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 17 2009]
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CROSSREFS
| Cf. A001044.
Cf. A100288 (primes of the form (1!)^2 + (2!)^2 + (3!)^2 +...+ (k!)^2).
Sequence in context: A066864 A181737 A116896 * A152479 A115961 A123137
Adjacent sequences: A061059 A061060 A061061 * A061063 A061064 A061065
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KEYWORD
| nonn
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AUTHOR
| Jason Earls (zevi_35711(AT)yahoo.com), May 27 2001
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EXTENSIONS
| More terms from T. D. Noe (noe(AT)sspectra.com), Dec 08 2004
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