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A052792
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Expansion of e.g.f.: x^2*(exp(x)-1)^4.
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1
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0, 0, 0, 0, 0, 0, 720, 10080, 87360, 604800, 3674160, 20512800, 108044640, 545688000, 2671036368, 12763951200, 59856451200, 276499641600, 1261691128944, 5699120476320, 25525119703200, 113497442856000, 501533701110288, 2204246146687200, 9641611208433600
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OFFSET
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0,7
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COMMENTS
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Original name: a simple grammar.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (30,-405,3250,-17247,63690,-167615,316350,-424428,394280,-240480,86400,-13824).
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FORMULA
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E.g.f.: x^2*exp(x)^4-4*x^2*exp(x)^3+6*x^2*exp(x)^2-4*exp(x)*x^2+x^2.
Recurrence: {a(1)=0, a(2)=0, a(4)=0, a(3)=0, a(5)=0, a(6)=720, (1200*n+840*n^2+240*n^3+576+24*n^4)*a(n)+(1200-50*n^4+100*n-850*n^2-400*n^3)*a(n+1)+(210*n^3+175*n^2+35*n^4-420*n)*a(n+2)+(10*n^2-40*n^3+40*n-10*n^4)*a(n+3)+(-n^2+n^4-2*n+2*n^3)*a(n+4)}.
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MAPLE
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spec := [S, {B=Set(Z, 1 <= card), S=Prod(Z, Z, B, B, B, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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PROG
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(PARI) a(n)={if(n>=2, 4!*n*(n-1)*stirling(n-2, 4, 2), 0)} \\ Andrew Howroyd, Aug 08 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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Name changed and terms a(21) and beyond from Andrew Howroyd, Aug 08 2020
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STATUS
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approved
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