A110669 Sequence is {a(4,n)}, where a(m,n) is defined at sequence A110665.

0, 1, 4, 7, 4, -11, -38, -70, -100, -130, -172, -238, -328, -429, -528, -627, -744, -897, -1086, -1292, -1496, -1700, -1928, -2204, -2528, -2875, -3220, -3565, -3940, -4375, -4870, -5394, -5916, -6438, -6996, -7626, -8328, -9065, -9800, -10535, -11312, -12173, -13118, -14104, -15088, -16072, -17104

Offset

0,3

Links

Table of n, a(n) for n=0..46.

Formula

Empirical g.f.: -x*(2*x-1) / ((x-1)^4*(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 := 4: 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[4, n], {n, 0, 46}] (* Jean-François Alcover, Mar 29 2020 *)

Crossrefs

Cf. A110665, A110666, A110667, A110668, A110670, A110671, A110672.

Sequence in context: A094692 A059139 A329740 * A106027 A101159 A339948

Adjacent sequences: A110666 A110667 A110668 * A110670 A110671 A110672

Keyword

easy,sign

Author

Leroy Quet, Aug 02 2005

Extensions

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

Status

approved