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A014606 a(n) = (3n)!/(6^n). 38
1, 1, 20, 1680, 369600, 168168000, 137225088000, 182509367040000, 369398958888960000, 1080491954750208000000, 4386797336285844480000000, 23934366266775567482880000000, 170891375144777551827763200000000, 1561776277448122046153927884800000000 (list; graph; refs; listen; history; text; internal format)
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 sn(0,1)-matrices with row sum s and column sum 1 is ,(sn)!/(s!)^n). - Shanzhen Gao, Feb 12 2010

REFERENCES

G. E. Andrews, R. Askey and R. Roy, Special Functions, Cambridge University Press, 1998.

Gao, Shanzhen, and Matheis, Kenneth, 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. 202 (2010), 45-53.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..165

J.-C. Novelli, 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

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)=if(n<0, 0, (3*n)!/6^n)

CROSSREFS

Cf. A000680.

Sequence in context: A177635 A177296 A177297 * A330196 A172556 A246619

Adjacent sequences:  A014603 A014604 A014605 * A014607 A014608 A014609

KEYWORD

nonn,easy

AUTHOR

BjornE (mdeans(AT)algonet.se)

STATUS

approved

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Last modified August 12 12:09 EDT 2020. Contains 336439 sequences. (Running on oeis4.)