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A052785
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a(n) = 5!*n*Stirling2(n-1, 5).
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1
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0, 0, 0, 0, 0, 0, 720, 12600, 134400, 1134000, 8341200, 56133000, 355291200, 2151864000, 12614281680, 72135063000, 404672486400, 2236228722000, 12209943566160, 66024457842600, 354214283304000, 1887999348060000, 10008933180578640, 52820388477271800, 277680637970208000
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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,-395,3000,-14523,46710,-100805,143700,-129076,65760,-14400).
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FORMULA
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E.g.f.: x*exp(x)^5-5*x*exp(x)^4+10*exp(x)^3*x-10*exp(x)^2*x+5*x*exp(x)-x.
Recurrence: {a(1)=0, a(2)=0, a(4)=0, a(3)=0, a(5)=0, a(6)=720, ( - 14400 - 27000*n^2 - 32880*n - 120*n^5 - 1800*n^4 - 10200*n^3)*a(n) + (42196*n^2 + 19454*n^3 + 32880*n + 274*n^5 + 3836*n^4)*a(n + 1) + ( - 13500*n - 13275*n^3 - 24075*n^2 - 225*n^5 - 2925*n^4)*a(n + 2) + (85*n^5 + 3400*n + 1020*n^4 + 4165*n^3 + 6630*n^2)*a(n + 3) + ( - 915*n^2 - 450*n - 615*n^3 - 15*n^5 - 165*n^4)*a(n + 4) + (n^5 + 10*n^4 + 35*n^3 + 50*n^2 + 24*n)*a(n + 5)}.
G.f.: 120*x^6*(2 - 5*x)*(3 - 30*x + 95*x^2 - 100*x^3 + 24*x^4)/((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x))^2.
E.g.f.: x*(exp(x) - 1)^5. (End)
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MAPLE
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spec := [S, {B=Set(Z, 1 <= card), S=Prod(Z, B, 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>=1, 5!*n*stirling(n-1, 5, 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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