OFFSET
1,8
LINKS
Alois P. Heinz, Rows n = 1..45, flattened
FORMULA
See program.
EXAMPLE
Triangle begins:
1;
0, 1;
0, 1, 1;
0, 2, 3, 1;
24, 6, 11, 6, 1;
120, 144, 50, 35, 10, 1;
MAPLE
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: T:= (n, k)-> `if`(k<0 or k>=n, 0, coeff(row(n)(x), x, k)*(n-1)!): seq(seq(T(n, k), k=0..n-1), n=1..12);
MATHEMATICA
row[n_] := Module[{f, 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}]; Table[a[k], {k, 0, n-1}] /. Solve[eq] // First]; Table[row[n]*(n-1)!, {n, 1, 12}] // Flatten (* Jean-François Alcover, Feb 04 2014, after Alois P. Heinz *)
CROSSREFS
Row sums are in A052593.
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Oct 03 2008
STATUS
approved