A145143 - OEIS

%I #9 May 09 2023 12:26:10

%S 1,1,2,6,144,1200,9960,89040,1231776,18325440,280100160,4415368320,

%T 78497147520,1538731434240,32250825734400,708789321676800,

%U 16531867860480000,410557135229337600,10800330695046144000,298418233851795456000,8641298765266642944000

%N 1st 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, 1) *(n-1)!): seq (a(n), n=2..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][[2]]*(n-1)!; Table[a[n], {n, 2, 23}] (* _Jean-François Alcover_, Feb 14 2014, after Maple *)

%Y Cf. A145142, A145153.

%K nonn

%O 2,3

%A _Alois P. Heinz_, Oct 03 2008