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%I #5 Feb 14 2014 08:57:34
%S 1,6,35,225,2464,29932,375164,4877100,73016856,1229669496,22393143552,
%T 430226343456,8838633396384,195021406776960,4592633620285440,
%U 114230969866103040,2991995263667137536,82505359191832358400
%N 3rd column of A145142.
%p row:= proc(n) option remember; local f,i,x; f:= unapply (simplify (sum ('cat (a||i) *x^i', 'i'=0..n-1) ), x); unapply (subs (solve ({seq(f(i+1)= coeftayl (x/ (1-x-x^4)/ (1-x)^i, x=0, n), i=0..n-1)}, {seq (cat (a||i), i=0..n-1)}), sum ('cat (a||i) *x^i', 'i'=0..n-1) ), x); end: a:= n-> `if` (n=0, 0, coeftayl (row(n)(x), x=0, 3) *(n-1)!): seq (a(n), n=4..25);
%t row[n_] := row[n] = Module[{f, a, eq}, f = Function[x, Sum[a[k]*x^k, {k, 0, n-1}]]; eq = Table[f[k+1] == SeriesCoefficient[x/(1-x-x^4)/(1-x)^k, {x, 0, n}], {k, 0, n-1}]; List @@ f[1] /. Solve[eq] // First]; a[n_] := row[n][[4]]*(n-1)!; Table[a[n], {n, 4, 25}] (* _Jean-François Alcover_, Feb 14 2014, after Maple *)
%Y Cf. A145153.
%K nonn
%O 4,2
%A _Alois P. Heinz_, Oct 03 2008
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