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A038845
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3-fold convolution of A000302 (powers of 4).
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35
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1, 12, 96, 640, 3840, 21504, 114688, 589824, 2949120, 14417920, 69206016, 327155712, 1526726656, 7046430720, 32212254720, 146028888064, 657129996288, 2937757630464, 13056700579840, 57724360458240, 253987186016256
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OFFSET
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0,2
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COMMENTS
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Also convolution of A002802 with A000984 (central binomial coefficients).
With a different offset, number of n-permutations of 5 objects u, v, w, z, x with repetition allowed, containing exactly two u's. - Zerinvary Lajos, Dec 29 2007
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LINKS
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FORMULA
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a(n) = (n+2)*(n+1)*2^(2*n-1).
G.f.: 1/(1-4*x)^3.
a(n) = binomial(n+2,n) * 4^n. - Rui Duarte, Oct 08 2011
Sum_{n>=0} 1/a(n) = 8 - 24*log(4/3).
Sum_{n>=0} (-1)^n/a(n) = 40*log(5/4) - 8. (End)
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MAPLE
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MATHEMATICA
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Table[4^n*Binomial[n+2, n], {n, 0, 30}] (* G. C. Greubel, Jul 20 2019 *)
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PROG
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(Sage) [4^(n-2)*binomial(n, 2) for n in range(2, 30)] # Zerinvary Lajos, Mar 11 2009
(GAP) List([0..30], n-> 4^n*Binomial(n+2, n) ); # G. C. Greubel, Jul 20 2019
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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), this sequence (q=4), A081135 (q=5), A081136 (q=6), A027474 (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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easy,nonn,changed
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AUTHOR
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STATUS
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approved
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