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A014606
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a(n) = (3n)!/(6^n).
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40
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1, 1, 20, 1680, 369600, 168168000, 137225088000, 182509367040000, 369398958888960000, 1080491954750208000000, 4386797336285844480000000, 23934366266775567482880000000, 170891375144777551827763200000000, 1561776277448122046153927884800000000
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OFFSET
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0,3
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COMMENTS
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a(n) is also the constant term in the product : product 1 <= i,j <= n, i different from j (1 - x_i/x_j)^3. - Sharon Sela (sharonsela(AT)hotmail.com), Feb 14 2002
a(n) is also the number of n by 3n (0,1)-matrices with row sum 3 and column sum 1. In general, the number of n by s*n (0,1)-matrices with row sum s and column sum 1 is (s*n)!/(s!)^n). - Shanzhen Gao, Feb 12 2010
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REFERENCES
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George E. Andrews, Richard Askey and Ranjan Roy, Special Functions, Cambridge University Press, 1998.
Shanzhen Gao and Kenneth Matheis, Closed formulas and integer sequences arising from the enumeration of (0,1)-matrices with row sum two and some constant column sums. In Proceedings of the Forty-First Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congr. Numer., Vol. 202 (2010), pp. 45-53.
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LINKS
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FORMULA
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Sum_{n>=0} 1/a(n) = (exp(6^(1/3)) + 2*exp(-6^(1/3)/2)*cos(3^(5/6)/2^(2/3)))/3.
Sum_{n>=0} (-1)^n/a(n) = (exp(-6^(1/3)) + 2*exp(6^(1/3)/2)*cos(3^(5/6)/2^(2/3)))/3. (End)
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MATHEMATICA
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nn=36; Select[Range[0, nn]!CoefficientList[Series[1/(1-x^3/3!), {x, 0, nn}], x], #>0&] (* Geoffrey Critzer, Jun 07 2014 *)
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PROG
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(PARI) a(n)=(3*n)!/6^n;
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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BjornE (mdeans(AT)algonet.se)
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STATUS
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approved
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