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A053526
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Number of bipartite graphs with 3 edges on nodes {1..n}.
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5
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0, 0, 0, 0, 16, 110, 435, 1295, 3220, 7056, 14070, 26070, 45540, 75790, 121121, 187005, 280280, 409360, 584460, 817836, 1124040, 1520190, 2026255, 2665355, 3464076, 4452800, 5666050, 7142850, 8927100, 11067966, 13620285
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OFFSET
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0,5
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REFERENCES
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R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.5.
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LINKS
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FORMULA
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a(n) = (n-3)*(n-2)*(n-1)*n*(n^2 + 3*n + 4)/48.
E.g.f.: x^4*(32 + 12*x + x^2)*exp(x)/48. - G. C. Greubel, May 15 2019
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MATHEMATICA
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Table[Binomial[n, 4]*(n^2+3*n+4)/2, {n, 0, 40}] (* G. C. Greubel, May 15 2019 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 0, 0, 0, 16, 110, 435}, 40] (* Harvey P. Dale, Nov 24 2022 *)
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PROG
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(PARI) {a(n) = binomial(n, 4)*(n^2+3*n+4)/2}; \\ G. C. Greubel, May 15 2019
(Magma) [Binomial(n, 4)*(n^2+3*n+4)/2: n in [0..40]]; // G. C. Greubel, May 15 2019
(Sage) [binomial(n, 4)*(n^2+3*n+4)/2 for n in (0..40)] # G. C. Greubel, May 15 2019
(GAP) List([0..40], n-> Binomial(n, 4)*(n^2+3*n+4)/2) # G. C. Greubel, May 15 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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