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a(n) = n*(n-1)*a(n-1)/2 + a(n-2), a(0) = 1, a(1) = 2.
(Formerly M0911 N0343)
2

%I M0911 N0343 #29 Sep 08 2022 08:44:28

%S 1,2,3,11,69,701,10584,222965,6253604,225352709,10147125509,

%T 558317255704,36859086001973,2875567025409598,261713458398275391,

%U 27482788698844325653,3298196357319717353751,448582187384180404435789,68636372866136921596029468

%N a(n) = n*(n-1)*a(n-1)/2 + a(n-2), a(0) = 1, a(1) = 2.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A001052/b001052.txt">Table of n, a(n) for n = 0..100</a>

%p a := proc (n) option remember;

%p if n < 2 then n+1

%p else binomial(n,2)*a(n-1)+a(n-2) fi;

%p end proc;

%p seq(a(n), n = 0..20); # _G. C. Greubel_, Sep 20 2019

%t t = {1, 2}; Do[AppendTo[t, n*(n-1)*t[[-1]]/2 + t[[-2]]], {n, 2, 20}] (* _T. D. Noe_, Jun 25 2012 *)

%o (PARI) a(n)=if(n<2,max(0,n+1),n*(n-1)*a(n-1)/2+a(n-2))

%o (Magma) I:=[1,2]; [n le 2 select I[n] else Binomial(n-1,2)*Self(n-1) + Self(n-2): n in [1..20]]; // _G. C. Greubel_, Sep 20 2019

%o (Sage)

%o def a(n):

%o if (n<2): return n+1

%o else: return binomial(n,2)*a(n-1)+a(n-2)

%o [a(n) for n in (0..20)] # _G. C. Greubel_, Sep 20 2019

%o (GAP) a:=[1,2];; for n in [3..20] do a[n]:=Binomial(n-1,2)*a[n-1]+a[n-2]; od; a; # _G. C. Greubel_, Sep 20 2019

%Y Cf. A001046.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _James A. Sellers_, Sep 19 2000