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A053527 Number of bipartite graphs with 4 edges on nodes {1..n}. 3
0, 0, 0, 0, 3, 140, 1125, 5355, 19075, 56133, 143955, 332475, 706860, 1404975, 2640638, 4733820, 8149050, 13543390, 21825450, 34227018, 52388985, 78463350, 115233195, 166252625, 236008773, 330108075, 455489125, 620664525, 835994250 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

REFERENCES

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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

FORMULA

a(n) = (n-3)*(n-2)*(n-1)*n*(n+2)*(n^3-5*n-36)/384.

G.f.: x^4*(3+113*x-27*x^2+18*x^3-2*x^4)/(1-x)^9. [Colin Barker, May 08 2012]

MATHEMATICA

CoefficientList[Series[x^4*(3+113*x-27*x^2+18*x^3-2*x^4)/(1-x)^9, {x, 0, 30}], x] (* Vincenzo Librandi, May 08 2012 *)

PROG

(MAGMA) [((n^5-4*n^4-n^3+16*n^2-12*n)*(n^3-5*n-36))/384: n in [0..30]]; // Vincenzo Librandi, May 08 2012

CROSSREFS

Cf. A000217 (1 edge), A050534 (2 edges), A053526 (3 edges).

Sequence in context: A139956 A236193 A070322 * A195632 A152504 A191958

Adjacent sequences:  A053524 A053525 A053526 * A053528 A053529 A053530

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jan 16 2000

STATUS

approved

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Last modified October 18 07:00 EDT 2018. Contains 316307 sequences. (Running on oeis4.)