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A110668 Sequence is {a(3,n)}, where a(m,n) is defined at sequence A110665.

%I A110668 #16 Sep 04 2017 23:29:39
%S A110668 0,1,3,3,-3,-15,-27,-32,-30,-30,-42,-66,-90,-101,-99,-99,-117,-153,
%T A110668 -189,-206,-204,-204,-228,-276,-324,-347,-345,-345,-375,-435,-495,
%U A110668 -524,-522,-522,-558,-630,-702,-737,-735,-735,-777,-861,-945,-986,-984,-984,-1032,-1128,-1224,-1271,-1269,-1269,-1323,-1431
%N A110668 Sequence is {a(3,n)}, where a(m,n) is defined at sequence A110665.
%H A110668 Michael De Vlieger, <a href="/A110668/b110668.txt">Table of n, a(n) for n = 0..1000</a>
%F A110668 Conjecture: g.f.: x*(-1+2*x) / ( (x^2-x+1)^2*(x-1)^3 ). - _R. J. Mathar_, Oct 09 2013
%e A110668 a(0,n): 0,  1,  0, -3, -4, ...
%e A110668 a(1,n): 0,  1,  1, -2, -6, ...
%e A110668 a(2,n): 0,  1,  2,  0, -6, ...
%e A110668 a(3,n): 0,  1,  3,  3, -3, ...
%e A110668 a(4,n): 0,  1,  4,  7,  4, ...
%e A110668 Main diagonal of array is 0, 1, 2, 3, 4, ...
%p A110668 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 :
%p A110668 nmax := 100 : m := 3: a := A11066x(m,nmax) :
%p A110668 for n from 0 to nmax do printf("%d,",a[m,n]) ; od ; # _R. J. Mathar_, Sep 01 2006
%t A110668 a[m_, n_] := a[m, n] = Which[n == 0, 0, m == 0, n - Sum[ Binomial[2 n - k - 1, n - 1]*a[0, k], {k, 0, (n - 1)}], True, a[m - 1, n] + a[m, n - 1]]; Array[a[3, #] &, 54, 0] (* _Michael De Vlieger_, Sep 04 2017 *)
%Y A110668 Cf. A110665 - A110672.
%K A110668 easy,sign
%O A110668 0,3
%A A110668 _Leroy Quet_, Aug 02 2005
%E A110668 More terms from _R. J. Mathar_, Sep 01 2006