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A036226
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Expansion of 1/(1-7*x)^7.
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8
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1, 49, 1372, 28812, 504210, 7764834, 108707676, 1413199788, 17311697403, 201969803035, 2262061793992, 24471395771368, 256949655599364, 2628792630362724, 26287926303627240, 257621677775546952
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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>=6) of 8 objects: r, s, t, u, v, z, x, y with repetition allowed, containing exactly six (6) u's. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 16 2008
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..400
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FORMULA
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a(n) = 7^n*binomial(n+6, 6). G.f.: 1/(1-7*x)^7.
a(0)=1, a(1)=49, a(2)=1372, a(3)=28812, a(4)=504210, a(5)=7764834, a(6)=108707676, a(n)=49*a(n-1)-1029*a(n-2)+12005*a(n-3)-84035*a(n-4)+352947*a(n-5)- 823543*a(n-6)+ 823543*a(n-7). - Harvey P. Dale, Feb 21 2013
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MAPLE
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seq(binomial(n+6, 6)*7^n, n=0..16); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 16 2008
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MATHEMATICA
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CoefficientList[Series[1/(1-7x)^7, {x, 0, 20}], x] (* or *) LinearRecurrence[ {49, -1029, 12005, -84035, 352947, -823543, 823543}, {1, 49, 1372, 28812, 504210, 7764834, 108707676}, 20] (* Harvey P. Dale, Feb 21 2013 *)
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PROG
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(Sage)[lucas_number2(n, 7, 0)*binomial(n, 6)/7^6 for n in xrange(6, 22)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 13 2009]
(MAGMA) [7^n* Binomial(n+6, 6): n in [0..20]]; // Vincenzo Librandi, Oct 12 2011
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CROSSREFS
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A036084.
Sequence in context: A011001 A115999 A012238 * A032655 A001458 A004374
Adjacent sequences: A036223 A036224 A036225 * A036227 A036228 A036229
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang
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STATUS
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approved
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