A275330 - OEIS

%I #12 Feb 26 2020 06:43:15

%S 1,1,3,2,3,7,4,6,7,19,9,12,14,19,46,20,27,28,38,46,129,48,60,63,76,92,

%T 129,337,115,144,140,171,184,258,337,939,286,345,336,380,414,516,674,

%U 939,2581,719,858,805,912,920,1161,1348,1878,2581,7238

%N Triangle read by rows, T(n,k) = t(n-k+1)*Sum_{d|k} d*t(d) with t = A000081, for n>=1 and 1<=k<=n.

%e Table starts:

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

%e [1] [1] 1

%e [2] [1, 3] 4

%e [3] [2, 3, 7] 12

%e [4] [4, 6, 7, 19] 36

%e [5] [9, 12, 14, 19, 46] 100

%e [6] [20, 27, 28, 38, 46, 129] 288

%e [7] [48, 60, 63, 76, 92, 129, 337] 805

%e [8] [115, 144, 140, 171, 184, 258, 337, 939] 2288

%e [9] [286, 345, 336, 380, 414, 516, 674, 939, 2581] 6471

%o (Sage)

%o @cached_function

%o def t():

%o     n = 1

%o     b = [0,1]

%o     while True:

%o         S = [b[n-k+1]*sum(d*b[d] for d in divisors(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..12): print(next(t_list))

%Y T(n,0) = A000081(n).

%Y T(n,n) = A209397(n).

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

%Y Cf. A275331.

%K nonn,tabl

%O 1,3

%A _Peter Luschny_, Aug 18 2016