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A275331 Triangle read by rows, T(n,k) = k*Sum_{m=1..n/k} t(k)*t(n-k*m+1) with t = A000081, for n>=1 and 1<=k<=n.

%I A275331 #11 Feb 26 2020 06:43:22
%S A275331 1,2,2,4,2,6,8,6,6,16,17,10,12,16,45,37,24,30,32,45,120,85,50,60,64,
%T A275331 90,120,336,200,120,132,160,180,240,336,920,486,280,318,336,405,480,
%U A275331 672,920,2574,1205,692,750,800,945,1080,1344,1840,2574,7190
%N A275331 Triangle read by rows, T(n,k) = k*Sum_{m=1..n/k} t(k)*t(n-k*m+1) with t = A000081, for n>=1 and 1<=k<=n.
%e A275331 Triangle starts:
%e A275331 [n] [k=1,2,...] row sum
%e A275331 [1] [1] 1
%e A275331 [2] [2, 2] 4
%e A275331 [3] [4, 2, 6] 12
%e A275331 [4] [8, 6, 6, 16] 36
%e A275331 [5] [17, 10, 12, 16, 45] 100
%e A275331 [6] [37, 24, 30, 32, 45, 120] 288
%e A275331 [7] [85, 50, 60, 64, 90, 120, 336] 805
%e A275331 [8] [200, 120, 132, 160, 180, 240, 336, 920] 2288
%e A275331 [9] [486, 280, 318, 336, 405, 480, 672, 920, 2574] 6471
%o A275331 (Sage)
%o A275331 @cached_function
%o A275331 def t():
%o A275331     n = 1
%o A275331     b = [0,1]
%o A275331     while True:
%o A275331         S = [k*sum(b[k]*b[n-k*m+1] for m in (1..n//k)) for k in (1..n)]
%o A275331         b.append(sum(S)//n)
%o A275331         yield S
%o A275331         n += 1
%o A275331 t_list = t()
%o A275331 for n in (1..8): print(next(t_list))
%Y A275331 T(n,0) = A087803(n).
%Y A275331 T(n,n) = A055544(n).
%Y A275331 Sum_k T(n,k) = A095350(n+1).
%Y A275331 Cf. A000081, A275330.
%K A275331 nonn,tabl
%O A275331 1,2
%A A275331 _Peter Luschny_, Aug 18 2016