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Search: id:A061062
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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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+0
4
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| 1, 2, 6, 42, 618, 15018, 533418, 25935018, 1651637418, 133333531818, 13301522971818, 1606652445211818, 231049185247771818, 39006837228880411818, 7639061293780877851818, 1717651314017980301851818
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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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FORMULA
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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
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a(3)=0!*0!+1!*1!+2!*2!=6.
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MAPLE
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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
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s=0; Table[s=s+(n!)^2, {n, 0, 20}]
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CROSSREFS
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Cf. A001044.
Cf. A100288 (primes of the form (1!)^2 + (2!)^2 + (3!)^2 +...+ (k!)^2).
Adjacent sequences: A061059 A061060 A061061 this_sequence A061063 A061064 A061065
Sequence in context: A115974 A066864 A116896 this_sequence A115961 A123137 A014117
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KEYWORD
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nonn
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AUTHOR
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Jason Earls (zevi_35711(AT)yahoo.com), May 27 2001
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EXTENSIONS
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More terms from T. D. Noe (noe(AT)sspectra.com), Dec 08 2004
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