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%I #18 Sep 08 2022 08:44:59
%S 2,3,10,54,408,3960,46800,650160,10362240,186157440,3719520000,
%T 81789523200,1962469555200,51017981414400,1428416301312000,
%U 42851181364992000,1371216880889856000,46621018262827008000
%N a(n) = (1 + 2^n) * n!.
%H G. C. Greubel, <a href="/A052561/b052561.txt">Table of n, a(n) for n = 0..400</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=503">Encyclopedia of Combinatorial Structures 503</a>
%F E.g.f.: (2-3*x)/((1-x)*(1-2*x)).
%F a(n) = 3*n*a(n-1) - 2*n*(n-1)*a(n-2), with a(0)=2, a(1)=3.
%F a(n) = A000051(n)*A000142(n). - _Michel Marcus_, May 05 2019
%p spec := [S,{S=Union(Sequence(Z),Sequence(Union(Z,Z)))},labeled]: seq(combstruct[count](spec, size=n), n=0..20);
%t Table[(1+2^n)*n!, {n,0,20}] (* _G. C. Greubel_, May 05 2019 *)
%o (PARI) {a(n) = (1+2^n)*n!}; \\ _G. C. Greubel_, May 05 2019
%o (Magma) [(1+2^n)*Factorial(n): n in [0..20]]; // _G. C. Greubel_, May 05 2019
%o (Sage) [(1+2^n)*factorial(n) for n in (0..20)] # _G. C. Greubel_, May 05 2019
%o (GAP) List([0..20], n-> (1+2^n)*Factorial(n)) # _G. C. Greubel_, May 05 2019
%Y Cf. A000051, A000142.
%K easy,nonn
%O 0,1
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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