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A054119
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a(n) = n! + (n-1)! + (n-2)!.
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4
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1, 2, 4, 9, 32, 150, 864, 5880, 46080, 408240, 4032000, 43908480, 522547200, 6745939200, 93884313600, 1401079680000, 22317642547200, 377917892352000, 6778983923712000, 128403161542656000, 2560949482291200000, 53645489280294912000, 1177524571957493760000, 27027108408834293760000
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OFFSET
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0,2
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COMMENTS
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In factorial base representation (A007623) the terms are written as: 1, 10, 20, 111, 1110, 11100, 111000, ... From a(3) = 9 = "111" onward each term begins always with three consecutive 1's, followed by n-3 zeros. - Antti Karttunen, Sep 24 2016
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LINKS
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FORMULA
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a(n) = (n+1)!*(H(n-1)+H(n+1)-H(n-2)-H(n))/2, n>1, where H(n) is the n-th harmonic number. [Gary Detlefs, Oct 04 2011]
E.g.f.: x + 1/(1-x) - x*log(1-x) = x^2/G(0)/2 where G(k) = 1 + (k+2)/(x - x*(k+1)/(x + k + 1 - x^4/(x^3 +(k+2)*(k+3)/G(k+1)))); (continued fraction, 3rd kind, 4-step). - Sergei N. Gladkovskii, Jul 06 2012
G.f.: G(0) where G(k) = 1 - x/(1 + x/(1 - x - (k+1)/( k+1 - x/Q))); (continued fraction, 3rd kind, 4-step). - Sergei N. Gladkovskii, Jul 28 2012
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MAPLE
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f:= n-> `if`(n<0, 0, n!):
seq(f(n)+f(n-1)+f(n-2), n=0..23);
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MATHEMATICA
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PROG
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(Magma) [1, 2], [Factorial(n)+Factorial(n-1)+Factorial(n-2): n in [2..20]]; // Vincenzo Librandi, Oct 05 2011
(PARI) f(n) = if (n<0, 0, n!);
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CROSSREFS
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Equals T(n, 3), array T as in A054115.
Row 6 of A276955 (from a(3)=9 onward).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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