A110667 Sequence is {a(2,n)}, where a(m,n) is defined at sequence A110665.
0, 1, 2, 0, -6, -12, -12, -5, 2, 0, -12, -24, -24, -11, 2, 0, -18, -36, -36, -17, 2, 0, -24, -48, -48, -23, 2, 0, -30, -60, -60, -29, 2, 0, -36, -72, -72, -35, 2, 0, -42, -84, -84, -41, 2, 0, -48, -96, -96, -47, 2, 0, -54, -108, -108, -53, 2, 0, -60, -120, -120, -59, 2, 0, -66, -132, -132, -65, 2, 0, -72, -144, -144, -71, 2, 0
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 := 2: 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_, n_] := a[m, n] = Which[n == 0, 0, m == 0, n - Sum[ Binomial[2 n - k - 1, n - 1]*a[0, k], {k, 0, (n - 1)}], True, a[m - 1, n] + a[m, n - 1]]; Array[a[2, #] &, 76, 0] (* Michael De Vlieger, Sep 04 2017 *)
Formula
Conjecture: g.f.: -x*(-1+2*x) / ( (x-1)^2*(x^2-x+1)^2 ). - R. J. Mathar, Oct 09 2013
Extensions
More terms from R. J. Mathar, Sep 01 2006