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A014606
a(n) = (3n)!/(6^n).
41
1, 1, 20, 1680, 369600, 168168000, 137225088000, 182509367040000, 369398958888960000, 1080491954750208000000, 4386797336285844480000000, 23934366266775567482880000000, 170891375144777551827763200000000, 1561776277448122046153927884800000000
OFFSET
0,3
COMMENTS
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
REFERENCES
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.
LINKS
J.-C. Novelli and J.-Y. Thibon, Hopf Algebras of m-permutations,(m+1)-ary trees, and m-parking functions, arXiv preprint arXiv:1403.5962 [math.CO], 2014-2020.
FORMULA
E.g.f. with interpolated zeros: 1/(1 - x^3/3!). - Geoffrey Critzer, Jun 07 2014
a(n) = A025035(n)*n! - Geoffrey Critzer, Jun 07 2014
a(n) = A089759(3,n). - R. J. Mathar, Nov 01 2015
From Amiram Eldar, Jan 26 2022: (Start)
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)
MATHEMATICA
nn=36; Select[Range[0, nn]!CoefficientList[Series[1/(1-x^3/3!), {x, 0, nn}], x], #>0&] (* Geoffrey Critzer, Jun 07 2014 *)
PROG
(PARI) a(n)=(3*n)!/6^n;
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
BjornE (mdeans(AT)algonet.se)
STATUS
approved