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 A283322 Row sums of triangle in A283321. 2
 1, 2, 4, 22, 149, 1186, 10807, 110762, 1260289, 15757714, 214703831, 3165856882, 50220944017, 852735163034, 15429720661279, 296365775922106, 6021825238479617, 129039801791351842, 2908148713706872999, 68758376703814729154, 1701649010958291917521, 43990236798804135274282 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Indranil Ghosh, Table of n, a(n) for n = 0..400 G. N. Bakare, S. O. Makanjuola, Some Results on Properties of Alternating Semigroups, Nigerian Journal of Mathematics and Applications Volume 24,(2015), 184-192. FORMULA Bakare et al. give a formula, see Theorem 3.2. EXAMPLE Row 3 of triangle A283321: 1, 3, 3, 9. So a(3) = 1 + 3 + 3 + 9 = 22. - Indranil Ghosh, Mar 16 2017 MATHEMATICA 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 *) PROG (PARI) 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, 21, print1(sum(k=0, n, t(n, k)), ", "))} \\ Indranil Ghosh, Mar 16 2017 (Python) import math f=math.factorial def C(n, r): return f(n)/f(r)/f(n - r) def T(n, k): ....if k==n: return f(n)/2 ....elif k==n-1: return n**2 * f(n - 1) / 2 ....else: return C(n, k)**2 * f(k) i=0 l=[] for n in range(0, 401): ....for k in range(0, n+1): ........if n<2: l+=[1, ] ........else: l+=[T(n, k), ] ....print str(i)+" "+str(sum(l)) ....l=[] ....i+=1 # Indranil Ghosh, Mar 16 2017 CROSSREFS Cf. A283321. Sequence in context: A309741 A110130 A259116 * A019025 A264729 A192332 Adjacent sequences:  A283319 A283320 A283321 * A283323 A283324 A283325 KEYWORD nonn AUTHOR N. J. A. Sloane, Mar 15 2017 STATUS approved

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Last modified April 5 13:02 EDT 2020. Contains 333241 sequences. (Running on oeis4.)