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A275330 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.

%I A275330 #12 Feb 26 2020 06:43:15
%S A275330 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 A275330 129,337,115,144,140,171,184,258,337,939,286,345,336,380,414,516,674,
%U A275330 939,2581,719,858,805,912,920,1161,1348,1878,2581,7238
%N A275330 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 A275330 Table starts:
%e A275330 [n] [k=1,2,...] row sum
%e A275330 [1] [1] 1
%e A275330 [2] [1, 3] 4
%e A275330 [3] [2, 3, 7] 12
%e A275330 [4] [4, 6, 7, 19] 36
%e A275330 [5] [9, 12, 14, 19, 46] 100
%e A275330 [6] [20, 27, 28, 38, 46, 129] 288
%e A275330 [7] [48, 60, 63, 76, 92, 129, 337] 805
%e A275330 [8] [115, 144, 140, 171, 184, 258, 337, 939] 2288
%e A275330 [9] [286, 345, 336, 380, 414, 516, 674, 939, 2581] 6471
%o A275330 (Sage)
%o A275330 @cached_function
%o A275330 def t():
%o A275330     n = 1
%o A275330     b = [0,1]
%o A275330     while True:
%o A275330         S = [b[n-k+1]*sum(d*b[d] for d in divisors(k)) for k in (1..n)]
%o A275330         b.append(sum(S)//n)
%o A275330         yield S
%o A275330         n += 1
%o A275330 t_list = t()
%o A275330 for n in (1..12): print(next(t_list))
%Y A275330 T(n,0) = A000081(n).
%Y A275330 T(n,n) = A209397(n).
%Y A275330 Sum_k T(n,k) = A095350(n+1).
%Y A275330 Cf. A275331.
%K A275330 nonn,tabl
%O A275330 1,3
%A A275330 _Peter Luschny_, Aug 18 2016