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A027474
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a(n) = 7^(n-2) * C(n,2).
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19
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1, 21, 294, 3430, 36015, 352947, 3294172, 29647548, 259416045, 2219448385, 18643366434, 154231485954, 1259557135291, 10173346092735, 81386768741880, 645668365352248, 5084638377148953, 39779817891812397, 309398583602985310
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OFFSET
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2,2
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COMMENTS
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7th binomial transform of (0,0,1,0,0,0,........). Starting at 1, the three-fold convolution of A000420 (powers of 7). - Paul Barry, Mar 08 2003
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LINKS
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FORMULA
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G.f.: x^2 / (1-7*x)^3.
a(n) = 21*a(n-1) - 147*a(n-2) + 343*a(n-3), a(0) = a(1) = 0, a(2) = 1. (End)
Numerators of sequence a[3,n] in (a[i,j])^3 where a[i,j] = binomial(i-1, j-1)/2^(i-1) if j<=i, 0 if j>i.
Sum_{n>=2} 1/a(n) = 14 - 84*log(7/6).
Sum_{n>=2} (-1)^n/a(n) = 112*log(8/7) - 14. (End)
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MAPLE
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MATHEMATICA
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Table[7^(n-2) Binomial[n, 2], {n, 2, 20}] (* Harvey P. Dale, Sep 25 2011 *)
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PROG
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(Sage) [7^(n-2)*binomial(n, 2) for n in range(2, 21)] # Zerinvary Lajos, Mar 13 2009
(Magma) [7^(n-2)* Binomial(n, 2): n in [2..20]]; /* Vincenzo Librandi, Oct 12 2011 */
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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), this sequence (q=7), A081138 (q=8), A081139 (q=9), A081140 (q=10), A081141 (q=11), A081142 (q=12), A027476 (q=15).
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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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