A110668 Sequence is {a(3,n)}, where a(m,n) is defined at sequence A110665.

0, 1, 3, 3, -3, -15, -27, -32, -30, -30, -42, -66, -90, -101, -99, -99, -117, -153, -189, -206, -204, -204, -228, -276, -324, -347, -345, -345, -375, -435, -495, -524, -522, -522, -558, -630, -702, -737, -735, -735, -777, -861, -945, -986, -984, -984, -1032, -1128, -1224, -1271, -1269, -1269, -1323, -1431

Offset: 0

Author

Leroy Quet, Aug 02 2005

Keywords

• easy
• sign

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

Crossrefs

Cf. A110665 - A110672.

Programs

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 := 3: 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[3, #] &, 54, 0] (* Michael De Vlieger, Sep 04 2017 *)

Formula

Conjecture: g.f.: x*(-1+2*x) / ( (x^2-x+1)^2*(x-1)^3 ). - R. J. Mathar, Oct 09 2013

Extensions

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