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Search: id:A005726
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| A005726 |
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Quadrinomial coefficients.
(Formerly M1643)
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+0
2
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| 1, 2, 6, 20, 65, 216, 728, 2472, 8451, 29050, 100298, 347568, 1208220, 4211312, 14712960, 51507280, 180642391, 634551606, 2232223626, 7862669700, 27727507521, 97884558992, 345891702456, 1223358393120, 4330360551700
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 78.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
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a(n)=sum{k=0..floor(n/2), C(n, k)C(n, 2k+1) }. - Paul Barry (pbarry(AT)wit.ie), May 15 2003
a(n)=Sum[(-1)^k binomial[n,k] binomial[2n-2-4k,n-1],{k,0,Floor[(n-1)/4]}]. - David Callan (callan(AT)stat.wisc.edu), Jul 03 2006
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MAPLE
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for n from 1 to 40 do printf(`%d, `, coeff(expand(sum(x^j, j=0..3)^n), x, n-1)) od:
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CROSSREFS
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Sequence in context: A132353 A052958 A053730 this_sequence A148473 A000718 A148474
Adjacent sequences: A005723 A005724 A005725 this_sequence A005727 A005728 A005729
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Aug 21 2000
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