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%I #18 Mar 29 2020 09:33:09
%S 0,1,7,25,59,98,104,7,-293,-926,-2064,-3945,-6897,-11349,-17829,
%T -26964,-39498,-56328,-78540,-107426,-144482,-191408,-250132,-322858,
%U -412114,-520775,-652061,-809537,-997143,-1219254,-1480740,-1786995,-2143935,-2557998,-3036180,-3586107,-4216107
%N Sequence is {a(7,n)}, where a(m,n) is defined in sequence A110665.
%F Empirical g.f.: x*(1-2*x) / ((1-x)^7*(1-x+x^2)^2). - _Colin Barker_, Jul 09 2016
%e a(0,n): 0, 1, 0, -3, -4,...
%e a(1,n): 0, 1, 1, -2, -6,...
%e a(2,n): 0, 1, 2, 0, -6,...
%e a(3,n): 0, 1, 3, 3, -3,...
%e a(4,n): 0, 1, 4, 7, 4,...
%e Main diagonal of array is 0, 1, 2, 3, 4,...
%p 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 := 7: a := A11066x(m,nmax) : for n from 0 to nmax do printf("%d,",a[m,n]) ; od ; # _R. J. Mathar_, Sep 01 2006
%t a[_, 0] = 0;
%t a[0, n_] := a[0, n] = If[n < 3, {0, 1, 0}[[n+1]], (n((n-2)a[0, n-1] - (n-1)a[0, n-2]))/((n-1)(n-2))];
%t a[m_, n_] := a[m, n] = a[m-1, n] + a[m, n-1];
%t Table[a[7, n], {n, 0, 36}] (* _Jean-François Alcover_, Mar 29 2020 *)
%Y Cf. A110665, A110666, A110667, A110668, A110669, A110670, A110671.
%K easy,sign
%O 0,3
%A _Leroy Quet_, Aug 02 2005
%E More terms from _R. J. Mathar_, Sep 01 2006
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