A114936
Number of connected (4,n)-hypergraphs (without empty edges).
Original entry on oeis.org
0, 1, 10, 135, 1992, 30166, 458885, 6965225, 105358102, 1588998756, 23915093535, 359444209015, 5397938190512, 81022969645346, 1215801458118985, 18240857019892005, 273644796626023722, 4104936328561231936
Offset: 0
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With[{nmax = 50}, CoefficientList[Series[(1/4!)*(Exp[15*x] - 4*Exp[8*x] + 6*Exp[7*x] - 3*Exp[6*x] + 12*Exp[5*x] - 24*Exp[4*x] + 23*Exp[3*x] - 11*Exp[2*x] + 6*Exp[x] - 6), {x, 0, nmax}], x] Range[0, nmax]!] (* G. C. Greubel, Oct 07 2017 *)
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x='x+O('x^50); concat([0], Vec(serlaplace((1/4!)*(exp(15*x) - 4*exp(8*x) + 6*exp(7*x) - 3*exp(6*x) + 12*exp(5*x) - 24*exp(4*x) + 23*exp(3*x) - 11*exp(2*x) + 6*exp(x) - 6)))) \\ G. C. Greubel, Oct 07 2017
A114935
Number of connected (3,n)-hypergraphs (without empty edges).
Original entry on oeis.org
0, 1, 6, 44, 332, 2476, 18136, 130824, 933372, 6610676, 46603616, 327603904, 2298933412, 16115938476, 112906938696, 790735321784, 5536710117452, 38763269947876, 271368229299376, 1899679393564464, 13298164198917492
Offset: 0
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With[{nmax = 50}, CoefficientList[Series[(1/3!)*(Exp[7*x] - 3*Exp[4*x] + 5*Exp[3*x] - 3*Exp[2*x] + 2*Exp[x] - 2), {x, 0, nmax}], x] Range[0, nmax]!] (* G. C. Greubel, Oct 07 2017 *)
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x='x+O('x^50); concat([0], Vec(serlaplace((1/3!)*(exp(7*x) -3*exp(4*x) +5*exp(3*x) -3*exp(2*x) +2*exp(x) - 2)))) \\ G. C. Greubel, Oct 07 2017
A114934
Number of connected (5,n)-hypergraphs (without empty edges and without multiple edges).
Original entry on oeis.org
0, 0, 0, 21, 2773, 148365, 5878391, 204819447, 6721694469, 214306917321, 6736603947907, 210284186632443, 6541309609120385, 203129541349695597, 6302428271530970943, 195459285517696665759, 6060542952694406463421
Offset: 0
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With[{nmax = 50}, CoefficientList[Series[(1/5!)*(Exp[31*x] - 5*Exp[16*x] - 10*Exp[15*x] - 10*Exp[10*x] + 20*Exp[9*x] + 40*Exp[8*x] + 65*Exp[7*x] - 30*Exp[6*x] - 96*Exp[5*x] - 45*Exp[4*x] + 20*Exp[3*x] + 50*Exp[2*x] + 24*Exp[x] - 24), {x, 0, nmax}], x] Range[0, nmax]!] (* G. C. Greubel, Oct 07 2017 *)
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x='x+O('x^50); concat([0,0,0], Vec(serlaplace((1/5!)*(exp(31*x) - 5*exp(16*x) - 10*exp(15*x) - 10*exp(10*x) + 20*exp(9*x) + 40*exp(8*x) + 65*exp(7*x) - 30*exp(6*x) - 96*exp(5*x) - 45*exp(4*x) + 20*exp(3*x) + 50*exp(2*x) + 24*exp(x) - 24)))) \\ G. C. Greubel, Oct 07 2017
A114933
Number of connected (4,n)-hypergraphs (without empty edges and without multiple edges).
Original entry on oeis.org
0, 0, 0, 32, 1094, 23055, 405475, 6575842, 102567444, 1569195485, 23775369725, 358461659952, 5391042181294, 80974624209115, 1215462744452775, 18238484835400862, 273628186560143144, 4104820038944901945
Offset: 0
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With[{nmax = 50}, CoefficientList[Series[(1/4!)*(Exp[15*x] - 4*Exp[8*x] - 6*Exp[7*x] - 3*Exp[6*x] + 12*Exp[5*x] + 12*Exp[4*x] - Exp[3*x] - 11*Exp[2*x] - 6*Exp[x] + 6), {x, 0, nmax}], x] Range[0, nmax]!] (* G. C. Greubel, Oct 07 2017 *)
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x='x+O('x^50); concat([0,0,0], Vec(serlaplace((1/4!)*(exp(15*x)-4*exp(8*x)-6*exp(7*x)-3*exp(6*x)+12*exp(5*x)+12*exp(4*x)-exp(3*x)-11*exp(2*x)-6*exp(x)+6)))) \\ G. C. Greubel, Oct 07 2017
A114932
Number of connected (3,n)-hypergraphs (without empty edges and without multiple edges).
Original entry on oeis.org
0, 0, 1, 25, 267, 2265, 17471, 128765, 927067, 6591505, 46545591, 327428805, 2298406067, 16114352345, 112902172111, 790721005645, 5536667136267, 38763140938785, 271367842141031, 1899678231827285, 13298160713181667
Offset: 0
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With[{nmax = 50}, CoefficientList[Series[(1/3!)*(Exp[7*x] - 3*Exp[4*x] - Exp[3*x] + 3*Exp[2*x] + 2*Exp[x] - 2), {x, 0, nmax}], x] Range[0, nmax]!] (* G. C. Greubel, Oct 07 2017 *)
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x='x+O('x^50); concat([0,0], Vec(serlaplace((1/3!)*(exp(7*x)-3*exp(4*x)-exp(3*x)+3*exp(2*x)+2*exp(x)-2)))) \\ G. C. Greubel, Oct 07 2017
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