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A003438
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Number of 5 X 5 matrices with nonnegative integer entries and row and column sums equal to n.
(Formerly M5381)
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4
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1, 120, 6210, 153040, 2224955, 22069251, 164176640, 976395820, 4855258305, 20856798285, 79315936751, 272095118010, 854560160105, 2486299719645, 6765755480415, 17356306529251, 42250330784180, 98137852369965
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OFFSET
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0,2
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COMMENTS
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Number of 5 X 5 stochastic matrices of integers.
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REFERENCES
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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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. P. Stanley, Enumerative Combinatorics, Wadsworth, Vol. 1, 1986, p. 234.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (17, -136, 680, -2380, 6188, -12376, 19448, -24310, 24310, -19448, 12376, -6188, 2380, -680, 136, -17, 1).
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FORMULA
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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.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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