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A291678 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of k-th power of continued fraction 1 + x/(1 + x^2/(1 + x^3/(1 + x^4/(1 + x^5/(1 + ...))))).

%I A291678 #20 Apr 01 2018 05:52:37
%S A291678 1,1,0,1,1,0,1,2,0,0,1,3,1,-1,0,1,4,3,-2,0,0,1,5,6,-2,-2,1,0,1,6,10,0,
%T A291678 -6,2,1,0,1,7,15,5,-11,0,5,-1,0,1,8,21,14,-15,-8,12,0,-2,0,1,9,28,28,
%U A291678 -15,-24,18,9,-8,0,0,1,10,36,48,-7,-48,15,32,-15,-6,2
%N A291678 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of k-th power of continued fraction 1 + x/(1 + x^2/(1 + x^3/(1 + x^4/(1 + x^5/(1 + ...))))).
%H A291678 Seiichi Manyama, <a href="/A291678/b291678.txt">Antidiagonals n = 0..139, flattened</a>
%F A291678 G.f. of column k: Product_{j>=1} ((1 - x^(5*j-2))*(1 - x^(5*j-3)) / ((1 - x^(5*j-1))*(1 - x^(5*j-4))))^k.
%e A291678 Square array begins:
%e A291678    1,  1,  1,  1,   1, ...
%e A291678    0,  1,  2,  3,   4, ...
%e A291678    0,  0,  1,  3,   6, ...
%e A291678    0, -1, -2, -2,   0, ...
%e A291678    0,  0, -2, -6, -11, ...
%Y A291678 Columns k=0..4 give A000007, A003823, A285442, A285443, A285444.
%Y A291678 Rows n=0..1 give A000012, A001477.
%Y A291678 Main diagonal gives A291679.
%Y A291678 Antidiagonal sums give A302016.
%Y A291678 Cf. A286509.
%K A291678 sign,tabl
%O A291678 0,8
%A A291678 _Seiichi Manyama_, Aug 29 2017