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A055007
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Number of nonnegative integer 4 X 4 matrices with no zero rows or columns and with sum of elements equal to n.
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0
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1, 0, 0, 0, 24, 528, 4648, 26224, 112666, 401424, 1246000, 3476368, 8905432, 21266208, 47875272, 102482048, 210000931, 414160240, 789572072, 1460372624, 2628456428, 4615495808, 7924479264, 13328517504, 21997272036, 35674700896
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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FORMULA
| Number of nonnegative integer p X q matrices with no zero rows or columns and with sum of elements equal to n is Sum_{k=0...q} (-1)^k*C(q, k)*m(p, q-k, n) where m(p, q, n)=Sum_{k=0..p} (-1)^k*C(p, k)*C((p-k)*q+n-1, n).
For p = q = 4 we get a(n) = (1/15!)*(n^15 + 120*n^14 + 6580*n^13 + 218400*n^12 + 4637542*n^11 + 61261200*n^10 + 423591740*n^9 + 164392800*n^8 - 17247717487*n^7 - 47940252360*n^6 + 346941238280*n^5 + 557885764800*n^4 - 4897231459056*n^3 + 8643549191040*n^2 - 5894285241600*n + 1307674368000).
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CROSSREFS
| Cf. A054688, A054974, A054975, A052366.
Sequence in context: A004383 A112390 A166757 * A014907 A121905 A192835
Adjacent sequences: A055004 A055005 A055006 * A055008 A055009 A055010
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), May 30 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 31 2000
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