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A052753
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Expansion of e.g.f.: log(1-x)^4.
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3
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0, 0, 0, 0, 24, 240, 2040, 17640, 162456, 1614816, 17368320, 201828000, 2526193824, 33936357312, 487530074304, 7463742249600, 121367896891776, 2089865973021696, 37999535417459712, 727710096185266176, 14642785817771802624, 308902349883623731200, 6818239581643475251200
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OFFSET
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0,5
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COMMENTS
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Previous name was: A simple grammar.
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LINKS
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FORMULA
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E.g.f.: log(-1/(-1+x))^4.
Recurrence: {a(1)=0, a(0)=0, a(2)=0, (1+4*n+6*n^2+4*n^3+n^4)*a(n+1) + (-4*n^3-15-18*n^2-28*n)*a(n+2) + (6*n^2+24*n+25)*a(n+3) + (-4*n-10)*a(n+4)+a(n+5), a(3)=0, a(4)=24}.
a(n) ~ (n-1)! * 2*log(n)*(2*log(n)^2 + 6*gamma*log(n) - Pi^2 + 6*gamma^2), where gamma is Euler-Mascheroni constant (A001620). - Vaclav Kotesovec, Sep 30 2013
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MAPLE
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spec := [S, {B=Cycle(Z), S=Prod(B, B, B, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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CoefficientList[Series[(Log[1-x])^4, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 30 2013 *)
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PROG
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(PARI) x='x+O('x^30); concat(vector(4), Vec(serlaplace((log(1-x))^4))) \\ G. C. Greubel, Aug 30 2018
(PARI) a(n) = {4!*stirling(n, 4, 1)*(-1)^n} \\ Andrew Howroyd, Jul 27 2020
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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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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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STATUS
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approved
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