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A053528 Number of bipartite graphs with 5 edges on nodes {1..n}. 2
0, 0, 0, 0, 0, 60, 1701, 14952, 81228, 331884, 1116675, 3256407, 8500734, 20306286, 45093048, 94189095, 186736368, 353904096, 644842674, 1134910242, 1936817820, 3215467584, 5207403663, 8245956642, 12793342716, 19481177100, 29161079805, 42967291185, 62393475690 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

REFERENCES

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

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

FORMULA

a(n) = (n-4)*(n-3)*(n-2)*(n-1)*n*(n^5 + 5*n^4 + 5*n^3 - 85*n^2 - 374*n - 960)/3840.

G.f.: x^5*(60+1041*x-459*x^2+411*x^3-129*x^4+21*x^5)/(1-x)^11. - Colin Barker, May 08 2012

E.g.f.: x^5*(1920 + 7152*x + 3280*x^2 + 560*x^3 + 40*x^4 + x^5)*exp(x)/3840. - G. C. Greubel, May 15 2019

MATHEMATICA

Table[Binomial[n, 5]*(n^5 +5*n^4 +5*n^3 -85*n^2 -374*n -960)/32, {n, 0, 30}] (* G. C. Greubel, May 15 2019 *)

PROG

(PARI) {a(n) = binomial(n, 5)*(n^5 +5*n^4 +5*n^3 -85*n^2 -374*n -960)/32}; \\ G. C. Greubel, May 15 2019

(MAGMA) [Binomial(n, 5)*(n^5 +5*n^4 +5*n^3 -85*n^2 -374*n -960)/32: n in [0..30]]; // G. C. Greubel, May 15 2019

(Sage) [binomial(n, 5)*(n^5 +5*n^4 +5*n^3 -85*n^2 -374*n -960)/32 for n in (0..30)] # G. C. Greubel, May 15 2019

(GAP) List([0..30], n-> Binomial(n, 5)*(n^5 +5*n^4 +5*n^3 -85*n^2 -374*n -960)/32) # G. C. Greubel, May 15 2019

CROSSREFS

Cf. A000217 (1 edge), A050534 (2 edges), A053526 (3 edges), A053527 (4 edges).

Sequence in context: A054331 A160349 A281373 * A269104 A017776 A035725

Adjacent sequences:  A053525 A053526 A053527 * A053529 A053530 A053531

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jan 16 2000

STATUS

approved

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Last modified April 11 00:03 EDT 2021. Contains 342877 sequences. (Running on oeis4.)