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%I #13 Mar 16 2017 15:51:23
%S 1,2,4,22,149,1186,10807,110762,1260289,15757714,214703831,3165856882,
%T 50220944017,852735163034,15429720661279,296365775922106,
%U 6021825238479617,129039801791351842,2908148713706872999,68758376703814729154,1701649010958291917521,43990236798804135274282
%N Row sums of triangle in A283321.
%H Indranil Ghosh, <a href="/A283322/b283322.txt">Table of n, a(n) for n = 0..400</a>
%H G. N. Bakare, S. O. Makanjuola, <a href="http://kwsman.com/articles/Revised%20Bakare.pdf">Some Results on Properties of Alternating Semigroups</a>, Nigerian Journal of Mathematics and Applications Volume 24,(2015), 184-192.
%F Bakare et al. give a formula, see Theorem 3.2.
%e Row 3 of triangle A283321: 1, 3, 3, 9. So a(3) = 1 + 3 + 3 + 9 = 22. - _Indranil Ghosh_, Mar 16 2017
%t T[n_, k_]:=If[k==n, (n !/2), If[k==n - 1, n^2*(n - 1)!/2, Binomial[n,k]^2 * k !]]; t[n_,k_]:=If[n<2, 1, T[n, k]]; For[n=0, n<=20, Print[Sum[t[n, k], {k, 0, n}]," "]; n++] (* _Indranil Ghosh_, Mar 16 2017 *)
%o (PARI) T(n,k) = if(k==n, (n!/2), if(k==n - 1, n^2*(n - 1)!/2, binomial(n, k)^2 * k!));
%o t(n,k) = if(n<2, 1, T(n, k));
%o {for(n=0, 21, print1(sum(k=0, n, t(n,k)),", "))} \\ _Indranil Ghosh_, Mar 16 2017
%o (Python)
%o import math
%o f=math.factorial
%o def C(n,r): return f(n)/f(r)/f(n - r)
%o def T(n,k):
%o ....if k==n: return f(n)/2
%o ....elif k==n-1: return n**2 * f(n - 1) / 2
%o ....else: return C(n, k)**2 * f(k)
%o i=0
%o l=[]
%o for n in range(0,401):
%o ....for k in range(0, n+1):
%o ........if n<2: l+=[1,]
%o ........else: l+=[T(n,k),]
%o ....print str(i)+" "+str(sum(l))
%o ....l=[]
%o ....i+=1 # _Indranil Ghosh_, Mar 16 2017
%Y Cf. A283321.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Mar 15 2017
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