A275331 - OEIS

%I #11 Feb 26 2020 06:43:22

%S 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 90,120,336,200,120,132,160,180,240,336,920,486,280,318,336,405,480,

%U 672,920,2574,1205,692,750,800,945,1080,1344,1840,2574,7190

%N 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 Triangle starts:

%e [n] [k=1,2,...] row sum

%e [1] [1] 1

%e [2] [2, 2] 4

%e [3] [4, 2, 6] 12

%e [4] [8, 6, 6, 16] 36

%e [5] [17, 10, 12, 16, 45] 100

%e [6] [37, 24, 30, 32, 45, 120] 288

%e [7] [85, 50, 60, 64, 90, 120, 336] 805

%e [8] [200, 120, 132, 160, 180, 240, 336, 920] 2288

%e [9] [486, 280, 318, 336, 405, 480, 672, 920, 2574] 6471

%o (Sage)

%o @cached_function

%o def t():

%o     n = 1

%o     b = [0,1]

%o     while True:

%o         S = [k*sum(b[k]*b[n-k*m+1] for m in (1..n//k)) for k in (1..n)]

%o         b.append(sum(S)//n)

%o         yield S

%o         n += 1

%o t_list = t()

%o for n in (1..8): print(next(t_list))

%Y T(n,0) = A087803(n).

%Y T(n,n) = A055544(n).

%Y Sum_k T(n,k) = A095350(n+1).

%Y Cf. A000081, A275330.

%K nonn,tabl

%O 1,2

%A _Peter Luschny_, Aug 18 2016