A110671 Sequence is {a(6,n)}, where a(m,n) is defined at sequence A110665.
0, 1, 6, 18, 34, 39, 6, -97, -300, -633, -1138, -1881, -2952, -4452, -6480, -9135, -12534, -16830, -22212, -28886, -37056, -46926, -58724, -72726, -89256, -108661, -131286, -157476, -187606, -222111, -261486, -306255, -356940, -414063, -478182, -549927, -630000, -719138, -818076
Offset: 0
Examples
a(0,n): 0, 1, 0, -3, -4,... a(1,n): 0, 1, 1, -2, -6,... a(2,n): 0, 1, 2, 0, -6,... a(3,n): 0, 1, 3, 3, -3,... a(4,n): 0, 1, 4, 7, 4,... Main diagonal of array is 0, 1, 2, 3, 4,...
Programs
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Maple
A11066x := proc(mmax,nmax) local a,i,j ; a := array(0..mmax,0..nmax) ; a[0,0] := 0 ; for i from 1 to nmax do a[0,i] := i-sum(binomial(2*i-k-1,i-1)*a[0,k],k=0..i-1) : od ; for j from 1 to mmax do a[j,0] := 0 ; for i from 1 to nmax do a[j,i] := a[j-1,i]+a[j,i-1] ; od ; od ; RETURN(a) ; end : nmax := 100 : m := 6: a := A11066x(m,nmax) : for n from 0 to nmax do printf("%d,",a[m,n]) ; od ; # R. J. Mathar, Sep 01 2006 -
Mathematica
a[_, 0] = 0; a[0, n_] := a[0, n] = If[n < 3, {0, 1, 0}[[n+1]], (n((n-2)a[0, n-1] - (n-1)a[0, n-2]))/((n-1)(n-2))]; a[m_, n_] := a[m, n] = a[m-1, n] + a[m, n-1]; Table[a[6, n], {n, 0, 38}] (* Jean-François Alcover, Mar 29 2020 *)
Formula
Empirical g.f.: -x*(2*x-1) / ((x-1)^6*(x^2-x+1)^2). - Colin Barker, Jul 02 2014
Extensions
More terms from R. J. Mathar, Sep 01 2006