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.

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, 129, 337, 115, 144, 140, 171, 184, 258, 337, 939, 286, 345, 336, 380, 414, 516, 674, 939, 2581, 719, 858, 805, 912, 920, 1161, 1348, 1878, 2581, 7238

Offset: 1

Author

Peter Luschny, Aug 18 2016

Keywords

• nonn
• tabl

Examples

			Table starts:
[n] [k=1,2,...] row sum
[1] [1] 1
[2] [1, 3] 4
[3] [2, 3, 7] 12
[4] [4, 6, 7, 19] 36
[5] [9, 12, 14, 19, 46] 100
[6] [20, 27, 28, 38, 46, 129] 288
[7] [48, 60, 63, 76, 92, 129, 337] 805
[8] [115, 144, 140, 171, 184, 258, 337, 939] 2288
[9] [286, 345, 336, 380, 414, 516, 674, 939, 2581] 6471
		

Crossrefs

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

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

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

Cf. A275331.

Programs

Sage

@cached_function
def t():
    n = 1
    b = [0,1]
    while True:
        S = [b[n-k+1]*sum(d*b[d] for d in divisors(k)) for k in (1..n)]
        b.append(sum(S)//n)
        yield S
        n += 1
t_list = t()
for n in (1..12): print(next(t_list))