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A111519
Sequence is {a(1,n)}, where a(m,n) is defined at sequence A111518.
5
1, 1, -2, -6, 1, 12, -50, -64, 517, -718, -4893, 27627, -20732, -464357, 2672305, -2162339, -62481580, 444310916, -765988257, -11093444366, 111888950896, -384937404033, -2094287782189, 37323429564497, -222553834299716, -59765515327025, 14271643579848985, -141966128047629231
OFFSET
0,3
EXAMPLE
a(0,n): 1,0,-3,-4,7,...
a(1,n): 1,1,-2,-6,1,...
a(2,n): 1,2,0,-6,-5,...
a(3,n): 1,3,3,-3,-8,...
a(4,n): 1,4,7,4,-4,...
Main diagonal is 1,1,0,-3,-4,..., which is 1 followed by sequence a(0,n).
MAPLE
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
MATHEMATICA
nmax = 27;
a[_, 0] = 1;
a[m_ /; m > 0, n_ /; n > 0] := a[m, n] = a[m - 1, n] + a[m, n - 1] ;
sol = Solve[Table[a[n + 1, n + 1] == a[0, n], {n, 0, nmax}], Table[a[0, n], {n, 1, nmax + 1}], Integers] // First;
Do[a[m, n] = a[m, n] /. sol, {m, 0, nmax}, {n, 0, nmax}];
Table[a[1, n], {n, 0, nmax}] (* Jean-François Alcover, Sep 21 2020 *)
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Leroy Quet, Aug 05 2005
EXTENSIONS
More terms from R. J. Mathar, Sep 26 2006
STATUS
approved