A110666 Sequence is {a(1,n)}, where a(m,n) is defined at sequence A110665.
0, 1, 1, -2, -6, -6, 0, 7, 7, -2, -12, -12, 0, 13, 13, -2, -18, -18, 0, 19, 19, -2, -24, -24, 0, 25, 25, -2, -30, -30, 0, 31, 31, -2, -36, -36, 0, 37, 37, -2, -42, -42, 0, 43, 43, -2, -48, -48, 0, 49, 49, -2, -54, -54, 0, 55, 55, -2, -60, -60, 0, 61, 61, -2, -66, -66, 0, 67, 67, -2, -72, -72, 0, 73, 73, -2, -78, -78, 0, 79, 79, -2, -84
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, ...
Links
- Michael De Vlieger, Table of n, a(n) for n = 0..1000
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 := 1: 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[m_, 0] := 0; a[n_, n_] := n; a[0, n_] := n - Sum[Binomial[2*n - k - 1, n - 1]* a[0, k], {k, 0, n - 1}]; a[m_, n_] := a[m, n] = a[m - 1, n] + a[m, n - 1]; Table[a[1, n], {n, 0, 50}] (* G. C. Greubel, Sep 03 2017 *)
Formula
From R. J. Mathar, Oct 09 2013: (Start)
Conjecture: G.f. x*(-1+2*x) / ( (x-1)*(x^2-x+1)^2 ).
Extensions
More terms from R. J. Mathar, Sep 01 2006