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%I #5 Feb 14 2014 08:57:38
%S 1,3,11,50,634,6804,71868,789984,11025936,174509280,2940903360,
%T 51707242080,987781034304,20520063789120,456583392034560,
%U 10712403843563520,265316096850923520,6948996535924162560
%N 2nd 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, 2) *(n-1)!): seq (a(n), n=3..23);
%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][[3]]*(n-1)!; Table[a[n], {n, 3, 23}] (* _Jean-François Alcover_, Feb 14 2014, after Maple *)
%Y Cf. A145153.
%K nonn
%O 3,2
%A _Alois P. Heinz_, Oct 03 2008
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