A111523 Sequence is {a(5,n)}, where a(m,n) is defined at sequence A111518.

1, 5, 12, 16, 12, 7, -42, -242, -183, -173, -5413, 6523, 37329, -375658, 977204, 4143218, -53311893, 210488510, 411432809, -10928034980, 66603480055, -51520031207, -2744112360076, 26933442266635, -98628074677603, -626803397046344, 12466676321155843, -88760048121704842

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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

A111523T := 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 := A111523T(nmax) ; m := 5 ; for n from 0 to nmax do printf("%d, ", a[m, 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[5, n], {n, 0, nmax}] (* Jean-François Alcover, Sep 21 2020 *)

Crossrefs

Cf. A111518, A111519, A111520, A111521, A111522.

Sequence in context: A314276 A056713 A110670 * A078231 A178469 A314277

Adjacent sequences: A111520 A111521 A111522 * A111524 A111525 A111526

Keyword

easy,sign

Author

Leroy Quet, Aug 05 2005

Extensions

More terms from R. J. Mathar, Sep 26 2006

Status

approved