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

0,3

Links

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

Formula

Conjecture: g.f.: x*(-1+2*x) / ( (x^2-x+1)^2*(x-1)^3 ). - 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 := 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 *)

Crossrefs

Cf. A110665 - A110672.

Sequence in context: A183554 A229847 A196529 * A367773 A176248 A290159

Adjacent sequences: A110665 A110666 A110667 * A110669 A110670 A110671

Keyword

easy,sign

Author

Leroy Quet, Aug 02 2005

Extensions

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

Status

approved