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A130744
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a(n) = n*(n+2)*n!.
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6
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0, 3, 16, 90, 576, 4200, 34560, 317520, 3225600, 35925120, 435456000, 5708102400, 80472268800, 1214269056000, 19527937228800, 333456963840000, 6025763487744000, 114887039275008000, 2304854534062080000
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OFFSET
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0,2
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COMMENTS
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For n >= 1, a(n) = number whose factorial base representation (A007623) begins with a double digit {n}{n}, which is followed by n-1 zeros. Viewed in that base, this sequence looks like this: 0, 11, 220, 3300, 44000, 550000, 6600000, 77000000, 880000000, 9900000000, AA000000000, BB0000000000, ... (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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0 = +a(n) * (+a(n+1) + 2*a(n+2) - 6*a(n+3) + a(n+4)) + a(n+1) * (+5*a(n+2) - 6*a(n+3) + a(n+4)) + a(n+2) * (+3*a(n+2) - a(n+4)) + a(n+3) * (+a(n+3)) if n>=0. - Michael Somos, Mar 26 2014
a(n) = n * (n! + (n+1)!) = n * A001048(n+1).
a(n) = (n+2)! - (n+1)! - n! [from Orlovsky's Mathematica-code].
(End)
Sum_{n>=1} 1/a(n) = (Ei(1) - gamma)/2 - 1/4, where Ei(1) = A091725 and gamma = A001620.
Sum_{n>=1} (-1)^(n+1)/a(n) = (gamma - Ei(-1))/2 - 1/e + 1/4, where Ei(-1) = -A099285 and e = A001113. (End)
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EXAMPLE
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G.f. = 3*x + 16*x^2 + 90*x^3 + 576*x^4 + 4200*x^5 + 34560*x^6 + ...
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MATHEMATICA
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PROG
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CROSSREFS
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Column 3 of A257503 (apart from initial zero. Equally, row 3 of A257505).
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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