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A110666 Sequence is {a(1,n)}, where a(m,n) is defined at sequence A110665.

%I A110666 #19 Sep 04 2017 23:30:01
%S A110666 0,1,1,-2,-6,-6,0,7,7,-2,-12,-12,0,13,13,-2,-18,-18,0,19,19,-2,-24,
%T A110666 -24,0,25,25,-2,-30,-30,0,31,31,-2,-36,-36,0,37,37,-2,-42,-42,0,43,43,
%U A110666 -2,-48,-48,0,49,49,-2,-54,-54,0,55,55,-2,-60,-60,0,61,61,-2,-66,-66,0,67,67,-2,-72,-72,0,73,73,-2,-78,-78,0,79,79,-2,-84
%N A110666 Sequence is {a(1,n)}, where a(m,n) is defined at sequence A110665.
%H A110666 Michael De Vlieger, <a href="/A110666/b110666.txt">Table of n, a(n) for n = 0..1000</a>
%F A110666 From _R. J. Mathar_, Oct 09 2013: (Start)
%F A110666 Conjecture: G.f. x*(-1+2*x) / ( (x-1)*(x^2-x+1)^2 ).
%F A110666 a(n) = -A010892(n-1) + A165202(n) -1. (End)
%e A110666 a(0,n): 0,  1,  0, -3, -4, ...
%e A110666 a(1,n): 0,  1,  1, -2, -6, ...
%e A110666 a(2,n): 0,  1,  2,  0, -6, ...
%e A110666 a(3,n): 0,  1,  3,  3, -3, ...
%e A110666 a(4,n): 0,  1,  4,  7,  4, ...
%e A110666 Main diagonal of array is 0, 1, 2, 3, 4, ...
%p A110666 A11066x := proc(mmax,nmax) local a,i,j ; a := array(0..mmax,0..nmax) ; a[0,0] := 0 ; for i from 1 to nmax do a[0,i] := i-sum(binomial(2*i-k-1,i-1)*a[0,k],k=0..i-1) : od ; for j from 1 to mmax do a[j,0] := 0 ; for i from 1 to nmax do a[j,i] := a[j-1,i]+a[j,i-1] ; od ; od ; RETURN(a) ; end : nmax := 100 : m := 1: a := A11066x(m,nmax) : for n from 0 to nmax do printf("%d,",a[m,n]) ; od ; # _R. J. Mathar_, Sep 01 2006
%t A110666 a[m_, 0] := 0; a[n_, n_] := n; a[0, n_] := n - Sum[Binomial[2*n - k - 1, n - 1]* a[0, k], {k, 0, n - 1}]; a[m_, n_] := a[m, n] = a[m - 1, n] + a[m, n - 1]; Table[a[1, n], {n, 0, 50}] (* _G. C. Greubel_, Sep 03 2017 *)
%Y A110666 Cf. A110665, A110667, A110668, A110669, A110670, A110671, A110672.
%K A110666 easy,sign
%O A110666 0,4
%A A110666 _Leroy Quet_, Aug 02 2005
%E A110666 More terms from _R. J. Mathar_, Sep 01 2006