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Search: id:A040075
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| A040075 |
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5-fold convolution of A000302 (powers of 4); expansion of 1/(1-4*x)^5. |
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+0
11
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| 1, 20, 240, 2240, 17920, 129024, 860160, 5406720, 32440320, 187432960, 1049624576, 5725224960, 30534533120, 159719096320, 821412495360, 4161823309824, 20809116549120, 102821517066240, 502682972323840
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Also convolution of A020920 with A000984 (central binomial coefficients).
With a different offset, number of n-permutations (n=5) of 5 objects u, v, w, z, x with repetition allowed, containing exactly four (4)u's. Example: a(1)=20 because we have uuuuv, uuuvu, uuvuu, uvuuu, vuuuu, uuuuw, uuuwu, uuwuu, uwuuu, wuuuu, uuuuz, uuuzu, uuzuu, uzuuu, zuuuu, uuuux, uuuxu, uuxuu, uxuuu and xuuuu. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 19 2008
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a(n)=binomial(n+4, 4)*4^n; G.f. 1/(1-4*x)^5.
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MAPLE
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seq(seq(binomial(i, j)*4^(i-4), j =i-4), i=4..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 03 2007
seq(binomial(n+4, 4)*4^n, n=0..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 19 2008
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CROSSREFS
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Cf. A000302, A020920, A000984.
Cf. A038231.
Sequence in context: A061139 A061121 A073398 this_sequence A138442 A140124 A123954
Adjacent sequences: A040072 A040073 A040074 this_sequence A040076 A040077 A040078
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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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