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A050929
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Number of directed multigraphs with loops on 4 nodes with n arcs.
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5
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1, 2, 11, 47, 198, 713, 2423, 7388, 21003, 55433, 137944, 324659, 729022, 1567139, 3242954, 6479759, 12547894, 23607614, 43267994, 77405064, 135435666, 232137202, 390371944, 644897542, 1047890293, 1676518363, 2643628813
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (x^26-x^25 + 4*x^24 + 18*x^23 + 63*x^22 + 151*x^21 + 402*x^20 + 790*x^19 + 1511*x^18 + 2353*x^17 + 3400*x^16 + 4296*x^15 + 5115*x^14 + 5266*x^13 + 5115*x^12 + 4296*x^11 + 3400*x^10 + 2353*x^9 + 1511*x^8 + 790*x^7 + 402*x^6 + 151*x^5 + 63*x^4 + 18*x^3 + 4*x^2-x + 1)/((x^4-1)^4*(x^3-1)^5*(x^2-1)^4*(x-1)^3).
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MAPLE
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gf:= (x^26-x^25 + 4*x^24 + 18*x^23 + 63*x^22 + 151*x^21 + 402*x^20 + 790*x^19 + 1511*x^18 + 2353*x^17 + 3400*x^16 + 4296*x^15 + 5115*x^14 + 5266*x^13 + 5115*x^12 + 4296*x^11 + 3400*x^10 + 2353*x^9 + 1511*x^8 + 790*x^7 + 402*x^6 + 151*x^5 + 63*x^4 + 18*x^3 + 4*x^2-x + 1)/((x^4-1)^4*(x^3-1)^5*(x^2-1)^4*(x-1)^3):
S:= series(gf, x, 101):
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MATHEMATICA
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nn = 30; n = 4; CoefficientList[Series[CycleIndex[ Join[PairGroup[SymmetricGroup[n], Ordered], Permutations[Range[n*(n - 1) + 1, n*(n - 1) + n]], 2], s] /. Table[s[i] -> 1/(1 - x^i), {i, 1, n^2 - n}], {x, 0, nn}], x] (* Geoffrey Critzer, Aug 07 2015*)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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