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%I #13 Sep 21 2020 08:37:54
%S 1,4,7,4,-4,-5,-49,-200,59,10,-5240,11936,30806,-412987,1352862,
%T 3166014,-57455111,263800403,200944299,-11339467789,77531515035,
%U -118123511262,-2692592328869,29677554626711,-125561516944238,-528175322368741,13093479718202187
%N Sequence is {a(4,n)}, where a(m,n) is defined at sequence A111518.
%e a(0,n): 1,0,-3,-4,7,...
%e a(1,n): 1,1,-2,-6,1,...
%e a(2,n): 1,2,0,-6,-5,...
%e a(3,n): 1,3,3,-3,-8,...
%e a(4,n): 1,4,7,4,-4,...
%e Main diagonal is 1,1,0,-3,-4,..., which is 1 followed by sequence a(0,n).
%p A111522T := proc(nmax) local a,m,n; a := array(0..nmax,0..nmax) ; for m from 0 to nmax do a[m,0] := 1 ; od ; for n from 1 to nmax do a[n,n] := a[0,n-1] ; for m from n+1 to nmax do a[m,n] := a[m-1,n]+a[m,n-1] ; od ; for m from n-1 to 0 by -1 do a[m,n] := a[m+1,n]-a[m+1,n-1] ; od ; od ; RETURN(a) ; end: nmax := 50 ; a := A111522T(nmax) ; m := 4 ; for n from 0 to nmax do printf("%d,",a[m,n]) ; od; # _R. J. Mathar_, Sep 26 2006
%t nmax = 26;
%t a[_, 0] = 1;
%t a[m_ /; m > 0, n_ /; n > 0] := a[m, n] = a[m - 1, n] + a[m, n - 1];
%t sol = Solve[Table[a[n + 1, n + 1] == a[0, n], {n, 0, nmax}], Table[a[0, n], {n, 1, nmax + 1}], Integers] // First;
%t Do[a[m, n] = a[m, n] /. sol, {m, 0, nmax}, {n, 0, nmax}];
%t Table[a[4, n], {n, 0, nmax}] (* _Jean-François Alcover_, Sep 21 2020 *)
%Y Cf. A111518, A111519, A111520, A111521, A111523.
%K easy,sign
%O 0,2
%A _Leroy Quet_, Aug 05 2005
%E More terms from _R. J. Mathar_, Sep 26 2006
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