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A081142
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12th binomial transform of (0,0,1,0,0,0,...).
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13
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0, 0, 1, 36, 864, 17280, 311040, 5225472, 83607552, 1289945088, 19349176320, 283787919360, 4086546038784, 57954652913664, 811365140791296, 11234286564802560, 154070215745863680, 2095354934143746048
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OFFSET
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0,4
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COMMENTS
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Starting at 1, the three-fold convolution of A001021 (powers of 12).
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LINKS
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FORMULA
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a(n) = 36*a(n-1) - 432*a(n-2) + 1728*a(n-3), a(0) = a(1) = 0, a(2) = 1.
a(n) = 12^(n-2)*binomial(n, 2).
G.f.: x^2/(1 - 12*x)^3.
Sum_{n>=2} 1/a(n) = 24 - 264*log(12/11).
Sum_{n>=2} (-1)^n/a(n) = 312*log(13/12) - 24. (End)
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MAPLE
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seq(coeff(series(x^2/(1-12*x)^3, x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Nov 24 2018
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MATHEMATICA
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LinearRecurrence[{36, -432, 1728}, {0, 0, 1}, 30] (* or *) Table[(n-1) (n-2) 3^(n-3) 2^(2n-7), {n, 20}] (* Harvey P. Dale, Jul 25 2013 *)
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PROG
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(PARI) vector(20, n, n--; 2^(2*n-5)*3^(n-2)*n*(n-1)) \\ G. C. Greubel, Nov 23 2018
(Sage) [2^(2*n-5)*3^(n-2)*n*(n-1) for n in range(20)] # G. C. Greubel, Nov 23 2018
(GAP) List([0..20], n->12^(n-2)*Binomial(n, 2)); # Muniru A Asiru, Nov 24 2018
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CROSSREFS
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Sequences similar to the form q^(n-2)*binomial(n, 2): A000217 (q=1), A001788 (q=2), A027472 (q=3), A038845 (q=4), A081135 (q=5), A081136 (q=6), A027474 (q=7), A081138 (q=8), A081139 (q=9), A081140 (q=10), A081141 (q=11), this sequence (q=12), A027476 (q=15).
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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