Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #16 Sep 04 2017 23:29:29
%S 0,1,2,0,-6,-12,-12,-5,2,0,-12,-24,-24,-11,2,0,-18,-36,-36,-17,2,0,
%T -24,-48,-48,-23,2,0,-30,-60,-60,-29,2,0,-36,-72,-72,-35,2,0,-42,-84,
%U -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
%N Sequence is {a(2,n)}, where a(m,n) is defined at sequence A110665.
%H Michael De Vlieger, <a href="/A110667/b110667.txt">Table of n, a(n) for n = 0..1000</a>
%F Conjecture: g.f.: -x*(-1+2*x) / ( (x-1)^2*(x^2-x+1)^2 ). - _R. J. Mathar_, Oct 09 2013
%e a(0,n): 0, 1, 0, -3, -4, ...
%e a(1,n): 0, 1, 1, -2, -6, ...
%e a(2,n): 0, 1, 2, 0, -6, ...
%e a(3,n): 0, 1, 3, 3, -3, ...
%e a(4,n): 0, 1, 4, 7, 4, ...
%e Main diagonal of array is 0, 1, 2, 3, 4, ...
%p 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 :
%p nmax := 100 : m := 2: a := A11066x(m,nmax) :
%p for n from 0 to nmax do printf("%d,",a[m,n]) ; od ; # _R. J. Mathar_, Sep 01 2006
%t 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 *)
%Y Cf. A110665 - A110672.
%K easy,sign
%O 0,3
%A _Leroy Quet_, Aug 02 2005
%E More terms from _R. J. Mathar_, Sep 01 2006