A110672 Sequence is {a(7,n)}, where a(m,n) is defined in sequence A110665.

0, 1, 7, 25, 59, 98, 104, 7, -293, -926, -2064, -3945, -6897, -11349, -17829, -26964, -39498, -56328, -78540, -107426, -144482, -191408, -250132, -322858, -412114, -520775, -652061, -809537, -997143, -1219254, -1480740, -1786995, -2143935, -2557998, -3036180, -3586107, -4216107

Offset

0,3

Links

Table of n, a(n) for n=0..36.

Formula

Empirical g.f.: x*(1-2*x) / ((1-x)^7*(1-x+x^2)^2). - Colin Barker, Jul 09 2016

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 := 7: 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[7, n], {n, 0, 36}] (* Jean-François Alcover, Mar 29 2020 *)

Crossrefs

Cf. A110665, A110666, A110667, A110668, A110669, A110670, A110671.

Sequence in context: A365444 A268239 A350222 * A213481 A266709 A162264

Adjacent sequences: A110669 A110670 A110671 * A110673 A110674 A110675

Keyword

easy,sign

Author

Leroy Quet, Aug 02 2005

Extensions

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

Status

approved