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.
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, 90, 120, 336, 200, 120, 132, 160, 180, 240, 336, 920, 486, 280, 318, 336, 405, 480, 672, 920, 2574, 1205, 692, 750, 800, 945, 1080, 1344, 1840, 2574, 7190
Offset: 1
Examples
Triangle starts: [n] [k=1,2,...] row sum [1] [1] 1 [2] [2, 2] 4 [3] [4, 2, 6] 12 [4] [8, 6, 6, 16] 36 [5] [17, 10, 12, 16, 45] 100 [6] [37, 24, 30, 32, 45, 120] 288 [7] [85, 50, 60, 64, 90, 120, 336] 805 [8] [200, 120, 132, 160, 180, 240, 336, 920] 2288 [9] [486, 280, 318, 336, 405, 480, 672, 920, 2574] 6471
Crossrefs
Programs
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Sage
@cached_function def t(): n = 1 b = [0,1] while True: S = [k*sum(b[k]*b[n-k*m+1] for m in (1..n//k)) for k in (1..n)] b.append(sum(S)//n) yield S n += 1 t_list = t() for n in (1..8): print(next(t_list))