%I #13 Sep 21 2020 08:37:36

%S 1,1,-2,-6,1,12,-50,-64,517,-718,-4893,27627,-20732,-464357,2672305,

%T -2162339,-62481580,444310916,-765988257,-11093444366,111888950896,

%U -384937404033,-2094287782189,37323429564497,-222553834299716,-59765515327025,14271643579848985,-141966128047629231

%N Sequence is {a(1,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 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 nmax = 27;

%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[1, n], {n, 0, nmax}] (* _Jean-François Alcover_, Sep 21 2020 *)

%Y Cf. A111518, A111520, A111521, A111522, A111523.

%K easy,sign

%O 0,3

%A _Leroy Quet_, Aug 05 2005

%E More terms from _R. J. Mathar_, Sep 26 2006