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

0,3

Links

Michael De Vlieger, Table of n, a(n) for n = 0..1000

Formula

Conjecture: g.f.: -x*(-1+2*x) / ( (x-1)^2*(x^2-x+1)^2 ). - R. J. Mathar, Oct 09 2013

Example

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, ...

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 *)

Crossrefs

Cf. A110665 - A110672.

Sequence in context: A335061 A350462 A357367 * A347929 A129877 A371913

Adjacent sequences: A110664 A110665 A110666 * A110668 A110669 A110670

Keyword

easy,sign

Author

Leroy Quet, Aug 02 2005

Extensions

More terms from R. J. Mathar, Sep 01 2006

Status

approved