cp's OEIS Frontend

A294947 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of exp(-Sum_{j>0} sigma_k(j)*x^j/j) in powers of x.

%I A294947 #13 Nov 13 2017 13:26:50
%S A294947 1,1,-1,1,-1,-2,1,-1,-4,-7,1,-1,-8,-23,-57,1,-1,-16,-73,-229,-541,1,
%T A294947 -1,-32,-227,-927,-2761,-7126,1,-1,-64,-697,-3757,-13969,-42615,
%U A294947 -108072,1,-1,-128,-2123,-15207,-70237,-254580,-758499,-1966034
%N A294947 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of exp(-Sum_{j>0} sigma_k(j)*x^j/j) in powers of x.
%F A294947 G.f. of column k: Product_{j>0} (1 - j^j*x^j)^(j^(k-1)).
%e A294947 Square array begins:
%e A294947       1,     1,      1,      1,       1, ...
%e A294947      -1,    -1,     -1,     -1,      -1, ...
%e A294947      -2,    -4,     -8,    -16,     -32, ...
%e A294947      -7,   -23,    -73,   -227,    -697, ...
%e A294947     -57,  -229,   -927,  -3757,  -15207, ...
%e A294947    -541, -2761, -13969, -70237, -351361, ...
%Y A294947 Columns k=0..2 give A294948, A292312, A294809.
%Y A294947 Rows n=0..1 give A000012, (-1)*A000012.
%Y A294947 Cf. A294946, A294951.
%K A294947 sign,tabl
%O A294947 0,6
%A A294947 _Seiichi Manyama_, Nov 11 2017