

A053526


Number of bipartite graphs with 3 edges on nodes {1..n}.


5



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

0,5


REFERENCES

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.5.


LINKS



FORMULA

a(n) = (n3)*(n2)*(n1)*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


MATHEMATICA

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 *)


PROG

(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


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



