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%I A111519 #13 Sep 21 2020 08:37:36
%S A111519 1,1,-2,-6,1,12,-50,-64,517,-718,-4893,27627,-20732,-464357,2672305,
%T A111519 -2162339,-62481580,444310916,-765988257,-11093444366,111888950896,
%U A111519 -384937404033,-2094287782189,37323429564497,-222553834299716,-59765515327025,14271643579848985,-141966128047629231
%N A111519 Sequence is {a(1,n)}, where a(m,n) is defined at sequence A111518.
%e A111519 a(0,n): 1,0,-3,-4,7,...
%e A111519 a(1,n): 1,1,-2,-6,1,...
%e A111519 a(2,n): 1,2,0,-6,-5,...
%e A111519 a(3,n): 1,3,3,-3,-8,...
%e A111519 a(4,n): 1,4,7,4,-4,...
%e A111519 Main diagonal is 1,1,0,-3,-4,..., which is 1 followed by sequence a(0,n).
%p A111519 A111519T := 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 := A111519T(nmax) ; r := 1 ; for n from 0 to nmax do printf("%d,",a[r,n]) ; od; # _R. J. Mathar_, Sep 26 2006
%t A111519 nmax = 27;
%t A111519 a[_, 0] = 1;
%t A111519 a[m_ /; m > 0, n_ /; n > 0] := a[m, n] = a[m - 1, n] + a[m, n - 1] ;
%t A111519 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 A111519 Do[a[m, n] = a[m, n] /. sol, {m, 0, nmax}, {n, 0, nmax}];
%t A111519 Table[a[1, n], {n, 0, nmax}] (* _Jean-François Alcover_, Sep 21 2020 *)
%Y A111519 Cf. A111518, A111520, A111521, A111522, A111523.
%K A111519 easy,sign
%O A111519 0,3
%A A111519 _Leroy Quet_, Aug 05 2005
%E A111519 More terms from _R. J. Mathar_, Sep 26 2006

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