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A054338
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8-fold convolution of A000302 (powers of 4).
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3
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1, 32, 576, 7680, 84480, 811008, 7028736, 56229888, 421724160, 2998927360, 20392706048, 133479530496, 845370359808, 5202279137280, 31213674823680, 183120225632256, 1052941297385472, 5946021444059136, 33033452466995200, 180814687187763200, 976399310813921280
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OFFSET
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0,2
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COMMENTS
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With a different offset, number of n-permutations (n>=7) of 5 objects: u, v, z, x, y with repetition allowed, containing exactly seven (7) u's. - Zerinvary Lajos, Jun 23 2008
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LINKS
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FORMULA
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a(n) = binomial(n+7, 7)*4^n.
G.f.: 1/(1-4*x)^8.
E.g.f.: (315 + 8820*x + 52920*x^2 + 117600*x^3 + 117600*x^4 + 56448*x^5 + 12544*x^6 + 1024*x^7)*exp(4*x)/315. - G. C. Greubel, Jul 21 2019
Sum_{n>=0} 1/a(n) = 20412*log(4/3) - 88067/15.
Sum_{n>=0} (-1)^n/a(n) = 437500*log(5/4) - 292873/3. (End)
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MAPLE
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MATHEMATICA
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Table[4^n*Binomial[n+7, 7], {n, 0, 20}] (* G. C. Greubel, Jul 21 2019 *)
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PROG
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(PARI) vector(20, n, n--; 4^n*binomial(n+7, 7)) \\ G. C. Greubel, Jul 21 2019
(GAP) List([0..20], n-> 4^n*Binomial(n+7, 7) ); # G. C. Greubel, Jul 21 2019
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CROSSREFS
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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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