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%I M5381 #34 Jun 25 2023 20:05:57
%S 1,120,6210,153040,2224955,22069251,164176640,976395820,4855258305,
%T 20856798285,79315936751,272095118010,854560160105,2486299719645,
%U 6765755480415,17356306529251,42250330784180,98137852369965
%N Number of 5 X 5 matrices with nonnegative integer entries and row and column sums equal to n.
%C Number of 5 X 5 stochastic matrices of integers.
%D D. M. Jackson and G. H. J. van Rees, The enumeration of generalized double stochastic nonnegative integer square matrices, SIAM J. Comput., 4 (1975), 474-477.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D R. P. Stanley, Enumerative Combinatorics, Wadsworth, Vol. 1, 1986, p. 234.
%H T. D. Noe, <a href="/A003438/b003438.txt">Table of n, a(n) for n = 0..1000</a>
%H D. M. Jackson & G. H. J. van Rees, <a href="/A002817/a002817.pdf">The enumeration of generalized double stochastic nonnegative integer square matrices</a>, SIAM J. Comput., 4.4 (1975), 474-477. (Annotated scanned copy)
%H M. L. Stein and P. R. Stein, <a href="/A001496/a001496.pdf">Enumeration of Stochastic Matrices with Integer Elements</a>, Report LA-4434, Los Alamos Scientific Laboratory of the University of California, Los Alamos, NM, Jun 1970. [Annotated scanned copy]
%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (17, -136, 680, -2380, 6188, -12376, 19448, -24310, 24310, -19448, 12376, -6188, 2380, -680, 136, -17, 1).
%F G.f.: (1 + 103*x + 4306*x^2 + 63110*x^3 + 388615*x^4 + 1115068*x^5 + 1575669*x^6 + 1115068*x^7 + 388615*x^8 + 63110*x^9 + 4306*x^10 + 103*x^11 + x^12)/(1-x)^17.
%F a(n) = Sum_{j=0..6} A005466(j) * binomial(4+j+n, 4+2*j). - _Andrew Howroyd_, Apr 09 2020
%t CoefficientList[Series[(1+103x+4306x^2+63110x^3+388615x^4+1115068x^5+ 1575669x^6+1115068x^7+388615x^8+63110x^9+4306x^10+103x^11+x^12)/ (1-x)^17,{x,0,30}],x] (* _Harvey P. Dale_, Aug 17 2013 *)
%Y Cf. A002817, A001496, A019298.
%Y Cf. A001496, A005466, A058391.
%Y Row n=5 of A257493.
%K nonn,easy,nice
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _Vladeta Jovovic_, Feb 06 2000
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