A110670 Sequence is {a(5,n)}, where a(m,n) is defined at sequence A110665.

0, 1, 5, 12, 16, 5, -33, -103, -203, -333, -505, -743, -1071, -1500, -2028, -2655, -3399, -4296, -5382, -6674, -8170, -9870, -11798, -14002, -16530, -19405, -22625, -26190, -30130, -34505, -39375, -44769, -50685, -57123, -64119, -71745, -80073, -89138, -98938, -109473, -120785, -132958

Offset

0,3

Links

Table of n, a(n) for n=0..41.

Formula

Empirical g.f.: x*(2*x-1) / ((x-1)^5*(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 := 5: 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[5, n], {n, 0, 41}] (* Jean-François Alcover, Mar 29 2020 *)

Crossrefs

Cf. A110665, A110666, A110667, A110668, A110669, A110671, A110672.

Sequence in context: A314275 A314276 A056713 * A111523 A078231 A178469

Adjacent sequences: A110667 A110668 A110669 * A110671 A110672 A110673

Keyword

easy,sign

Author

Leroy Quet, Aug 02 2005

Extensions

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

Status

approved