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%I #13 Aug 09 2020 00:32:32
%S 0,0,0,0,0,0,720,10080,87360,604800,3674160,20512800,108044640,
%T 545688000,2671036368,12763951200,59856451200,276499641600,
%U 1261691128944,5699120476320,25525119703200,113497442856000,501533701110288,2204246146687200,9641611208433600
%N Expansion of e.g.f.: x^2*(exp(x)-1)^4.
%C Original name: a simple grammar.
%H Andrew Howroyd, <a href="/A052792/b052792.txt">Table of n, a(n) for n = 0..1000</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=749">Encyclopedia of Combinatorial Structures 749</a>
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (30,-405,3250,-17247,63690,-167615,316350,-424428,394280,-240480,86400,-13824).
%F 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.
%F 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)}.
%F a(n) = n*A052776(n-1) = 4!*n*(n-1)*Stirling2(n-2,4) for n >= 2. - _Andrew Howroyd_, Aug 08 2020
%p 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);
%o (PARI) a(n)={if(n>=2, 4!*n*(n-1)*stirling(n-2,4,2), 0)} \\ _Andrew Howroyd_, Aug 08 2020
%Y Cf. A052760, A052776.
%K easy,nonn
%O 0,7
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E Name changed and terms a(21) and beyond from _Andrew Howroyd_, Aug 08 2020
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