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Search: id:A036071
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| A036071 |
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Expansion of 1/(1-5*x)^5. |
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+0
7
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| 1, 25, 375, 4375, 43750, 393750, 3281250, 25781250, 193359375, 1396484375, 9775390625, 66650390625, 444335937500, 2905273437500, 18676757812500, 118286132812500, 739288330078125, 4566192626953125, 27904510498046875
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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With a different offset, number of n-permutations (n=5) of 6 objects u, v, w, z, x, y with repetition allowed, containing exactly four (4)u's. Example: a(1)=25 because we have uuuuv, uuuvu, uuvuu, uvuuu, vuuuu, uuuuw, uuuwu, uuwuu, uwuuu, wuuuu, uuuuz, uuuzu, uuzuu, uzuuu, zuuuu, uuuux, uuuxu, uuxuu, uxuuu, xuuuu uuuuy, uuuyu, uuyuu, uyuuu, yuuuu. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 12 2008
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FORMULA
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a(n) = binomial(n+4, 4)*5^n; G.f. 1/(1-5*x)^5.
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MAPLE
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seq(binomial(n+4, 4)*5^n, n=0..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 12 2008
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PROGRAM
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(Other) SAGE: [lucas_number2(n, 5, 0)*binomial(n, 4)/5^4 for n in xrange(4, 23)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 12 2009]
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CROSSREFS
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A001787, A038846.
Sequence in context: A130052 A059255 A022749 this_sequence A094190 A069396 A125482
Adjacent sequences: A036068 A036069 A036070 this_sequence A036072 A036073 A036074
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KEYWORD
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easy,nonn
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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