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
Examples
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,...
Programs
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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 *)
Formula
Empirical g.f.: x*(1-2*x) / ((1-x)^7*(1-x+x^2)^2). - Colin Barker, Jul 09 2016
Extensions
More terms from R. J. Mathar, Sep 01 2006