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nmax = 26;
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[3, n], {n, 0, nmax}] (* Jean-François Alcover, Sep 21 2020 *)
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A111521T := 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 := A111521T(nmax) ; m := 3 ; for n from 0 to nmax do printf("%d, ", a[m, n]) ; od; - _# _R. J. Mathar_, Sep 26 2006
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Leroy Quet , Aug 05 2005
_Leroy Quet _ Aug 05 2005
A111521T := 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 := A111521T(nmax) ; m := 3 ; for n from 0 to nmax do printf("%d, ", a[m, n]) ; od; - _R. J. Mathar (mathar(AT)strw.leidenuniv.nl), _, Sep 26 2006
More terms from _R. J. Mathar (mathar(AT)strw.leidenuniv.nl), _, Sep 26 2006
Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> (listed in lieu of email address)
easy,sign,new
Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> (listed in lieu of email address)
easy,sign,new
Leroy Quet (qq-quet(AT)mindspring.com), Aug 05 2005