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%I #21 Sep 08 2022 08:45:13
%S 1,4,21,124,825,6186,51961,484968,4988241,56117710,685883121,
%T 9053657196,128397320233,1947359356866,31457343457065,539268744978256,
%U 9778739908939041,187018400758459158,3762370179964296001,79427814910357360020,1755772750650004800441
%N Number of functions of [n] to [n] that simultaneously avoid the patterns 112 and 221.
%H Vincenzo Librandi, <a href="/A093965/b093965.txt">Table of n, a(n) for n = 1..200</a>
%F a(n) = A093966(n, n).
%F From _Vaclav Kotesovec_, Nov 20 2012: (Start)
%F E.g.f.: x*(exp(x) - x)/(1-x)^2.
%F Recurrence: (n-1)*a(n) = n*(n+1)*a(n-1) - (n-1)*n*a(n-2) for n>2.
%F a(n) ~ n!*n*(e-1). (End)
%t Rest[CoefficientList[Series[x(E^x-x)/(1-x)^2, {x, 0, 20}], x]* Range[0, 20]!] (* _Vaclav Kotesovec_, Nov 20 2012 *)
%o (PARI) my(x='x+O('x^66)); Vec(serlaplace(x*(exp(x)-x)/(1-x)^2)) \\ _Joerg Arndt_, May 11 2013
%o (Magma) [n le 2 select 4^(n-1) else n*((n+1)*Self(n-1) - (n-1)*Self(n-2))/(n-1): n in [1..30]]; // _G. C. Greubel_, Dec 29 2021
%o (Sage) [factorial(n)*( x*(exp(x) -x)/(1-x)^2 ).series(x,n+1).list()[n] for n in (1..30)] # _G. C. Greubel_, Dec 29 2021
%Y Cf. A093966.
%K nonn
%O 1,2
%A _Ralf Stephan_, Apr 20 2004
%E Name changed by _Olivier Gérard_, Aug 06 2016
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