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A052571
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E.g.f. x^3/(1-x)^2.
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7
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0, 0, 0, 6, 48, 360, 2880, 25200, 241920, 2540160, 29030400, 359251200, 4790016000, 68497228800, 1046139494400, 16999766784000, 292919058432000, 5335311421440000, 102437979291648000, 2067966706950144000
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OFFSET
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0,4
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COMMENTS
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For n >= 3, a(n) = number whose factorial base representation (A007623) begins with digit {n-2} followed by n-1 zeros. Viewed in that base, this sequence looks like this: 0, 0, 0, 100, 2000, 30000, 400000, 5000000, 60000000, 700000000, 8000000000, 90000000000, A00000000000, B000000000000, ... (where "digits" A and B stand for placeholder values 10 and 11 respectively). - Antti Karttunen, May 07 2015
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LINKS
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FORMULA
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E.g.f.: x^3/(-1+x)^2.
Recurrence: {a(1)=0, a(0)=0, a(2)=0, a(3)=6, (1-n^2)*a(n)+(-2+n)*a(n+1)=0}.
For n >= 2, a(n) = (n-2)*n!.
Sum_{n>=3} (-1)^(n+1)/a(n) = -1/4 + gamma/2 - Ei(-1)/2 = -1/4 + (1/2)*A001620 + (1/2)*A099285. (End)
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MAPLE
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spec := [S, {S=Prod(Z, Z, Z, Sequence(Z), Sequence(Z))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
a:=n->add((n!), j=1..n-2):seq(a(n), n=0..21); # Zerinvary Lajos, Aug 27 2008
G(x):=x^3/(1-x)^2: f[0]:=G(x): for n from 1 to 21 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..19); # Zerinvary Lajos, Apr 01 2009
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MATHEMATICA
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PROG
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(Magma) [0, 0], [n*(n+1)*(n+2)*Factorial(n): n in [0..20]]; // Vincenzo Librandi, Oct 11 2011
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CROSSREFS
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Column 5 of A257503 (apart from zero terms. Equally, row 5 of A257505).
Cf. sequences with formula (n + k)*n! listed in A282466.
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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STATUS
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approved
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