A294609 - OEIS

A294609

Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} 1/(1-j*x^j)^(j^(k*j)) in powers of x.

%I #15 Nov 07 2017 08:30:51

%S 1,1,1,1,1,3,1,1,9,6,1,1,33,90,14,1,1,129,2220,1154,25,1,1,513,59178,

%T 264908,17427,56,1,1,2049,1594836,67176362,49163017,309117,97,1,1,

%U 8193,43048770,17181595604,152662625259,13120646934,6285102,198

%N Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} 1/(1-j*x^j)^(j^(k*j)) in powers of x.

%H Seiichi Manyama, <a href="/A294609/b294609.txt">Antidiagonals n = 0..52, flattened</a>

%F A(0,k) = 1 and A(n,k) = (1/n) * Sum_{j=1..n} (Sum_{d|j} d^(k*d+1+j/d)) * A(n-j,k) for n > 0.

%e Square array begins:

%e 1, 1, 1, 1, 1, ...

%e 3, 9, 33, 129, 513, ...

%e 6, 90, 2220, 59178, 1594836, ...

%e 14, 1154, 264908, 67176362, 17181595604, ...

%Y Columns k=0..2 give A006906, A294610, A294611.

%Y Rows n=0-1 give A000012.

%Y Cf. A294605.

%K nonn,tabl

%O 0,6

%A _Seiichi Manyama_, Nov 04 2017