A110671 Sequence is {a(6,n)}, where a(m,n) is defined at sequence A110665.

0, 1, 6, 18, 34, 39, 6, -97, -300, -633, -1138, -1881, -2952, -4452, -6480, -9135, -12534, -16830, -22212, -28886, -37056, -46926, -58724, -72726, -89256, -108661, -131286, -157476, -187606, -222111, -261486, -306255, -356940, -414063, -478182, -549927, -630000, -719138, -818076

Offset

0,3

Links

Table of n, a(n) for n=0..38.

Formula

Empirical g.f.: -x*(2*x-1) / ((x-1)^6*(x^2-x+1)^2). - Colin Barker, Jul 02 2014

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 := 6: 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[_, 0] = 0;
a[0, n_] := a[0, n] = If[n < 3, {0, 1, 0}[[n+1]], (n((n-2)a[0, n-1] - (n-1)a[0, n-2]))/((n-1)(n-2))];
a[m_, n_] := a[m, n] = a[m-1, n] + a[m, n-1];
Table[a[6, n], {n, 0, 38}] (* Jean-François Alcover, Mar 29 2020 *)

Crossrefs

Cf. A110665, A110666, A110667, A110668, A110669, A110670, A110672.

Sequence in context: A124353 A232336 A153126 * A134078 A323148 A181510

Adjacent sequences: A110668 A110669 A110670 * A110672 A110673 A110674

Keyword

easy,sign

Author

Leroy Quet, Aug 02 2005

Extensions

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

Status

approved