A110669 - OEIS

%I #15 Mar 29 2020 09:32:50

%S 0,1,4,7,4,-11,-38,-70,-100,-130,-172,-238,-328,-429,-528,-627,-744,

%T -897,-1086,-1292,-1496,-1700,-1928,-2204,-2528,-2875,-3220,-3565,

%U -3940,-4375,-4870,-5394,-5916,-6438,-6996,-7626,-8328,-9065,-9800,-10535,-11312,-12173,-13118,-14104,-15088,-16072,-17104

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

%F Empirical g.f.: -x*(2*x-1) / ((x-1)^4*(x^2-x+1)^2). - _Colin Barker_, Jul 02 2014

%e a(0,n): 0, 1, 0, -3, -4,...

%e a(1,n): 0, 1, 1, -2, -6,...

%e a(2,n): 0, 1, 2, 0, -6,...

%e a(3,n): 0, 1, 3, 3, -3,...

%e a(4,n): 0, 1, 4, 7, 4,...

%e Main diagonal of array is 0, 1, 2, 3, 4,...

%p 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

%t a[_, 0] = 0;

%t 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))];

%t a[m_, n_] := a[m, n] = a[m-1, n] + a[m, n-1];

%t Table[a[4, n], {n, 0, 46}] (* _Jean-François Alcover_, Mar 29 2020 *)

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

%K easy,sign

%O 0,3

%A _Leroy Quet_, Aug 02 2005

%E More terms from _R. J. Mathar_, Sep 01 2006