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 A111523 Sequence is {a(5,n)}, where a(m,n) is defined at sequence A111518. 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS 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

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Last modified September 18 19:15 EDT 2021. Contains 347534 sequences. (Running on oeis4.)