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A294250 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: exp(Product_{j=1..n} (1+x^j) - 1).

%I A294250 #27 Oct 27 2017 11:01:08
%S A294250 1,1,0,1,1,0,1,1,1,0,1,1,3,1,0,1,1,3,13,1,0,1,1,3,19,49,1,0,1,1,3,19,
%T A294250 97,261,1,0,1,1,3,19,121,681,1531,1,0,1,1,3,19,121,921,5971,9073,1,0,
%U A294250 1,1,3,19,121,1041,8491,50443,63393,1,0,1,1,3,19,121,1041
%N A294250 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: exp(Product_{j=1..n} (1+x^j) - 1).
%H A294250 Seiichi Manyama, <a href="/A294250/b294250.txt">Antidiagonals n = 0..139, flattened</a>
%F A294250 B(j,k) is the coefficient of Product_{i=1..k} (1+x^i).
%F A294250 A(0,k) = 1 and A(n,k) = (n-1)! * Sum_{j=1..min(A000217(k),n)} j*B(j,k)*A(n-j,k)/(n-j)! for n > 0.
%e A294250 Square array A(n,k) begins:
%e A294250    1, 1,   1,   1,   1, ...
%e A294250    0, 1,   1,   1,   1, ...
%e A294250    0, 1,   3,   3,   3, ...
%e A294250    0, 1,  13,  19,  19, ...
%e A294250    0, 1,  49,  97, 121, ...
%e A294250    0, 1, 261, 681, 921, ...
%Y A294250 Columns k=0..5 give A000007, A000012, A118589, A294251, A294252, A294253.
%Y A294250 Rows n=0 gives A000012.
%Y A294250 Main diagonal gives A293840.
%Y A294250 Cf. A070936, A294212, A294254.
%K A294250 nonn,tabl
%O A294250 0,13
%A A294250 _Seiichi Manyama_, Oct 26 2017