OFFSET
0,4
COMMENTS
LINKS
Alois P. Heinz, Rows n = 0..99, flattened
Alois P. Heinz, Animation of Pi*u_n(x) for n=0..15, x=-3..3
FORMULA
See program.
EXAMPLE
MAPLE
u:= proc(n) option remember; local f, i, x; f:= unapply(simplify(sum('cat(a||(2*i+1))*x^(2*i+1)', 'i'=0..n) ), x); unapply(subs(solve({f(1)=0, seq((D@@i)(f)(1)=`if`(i=1, -1, -(D@@i)(f)(0)), i=1..n)}, {seq(cat(a||(2*i+1)), i=0..n)}), sum('cat(a||(2*i+1))*x^(2*i+1)', 'i'=0..n) ), x); end: T:= (n, k)-> coeff(u(n)(x), x, 2*k+1): seq(seq(numer(T(n, k)), k=0..n), n=0..9);
MATHEMATICA
f[x_] := Sum[a[2i+1] x^(2i+1), {i, 0, n}];
u[n_] := u[n] = Function[x, f[x] /. Solve[Join[{f[1] == 0}, Table[(D[f[x], {x, i}] /. x -> 1) == If[i == 1, -1, -(D[f[x], {x, i}] /. x -> 0)], {i, 1, n}]]][[1]]];
T[n_, k_] := Coefficient[u[n][x], x, 2k+1];
Table[Numerator[T[n, k]], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Feb 12 2014, translated from Maple, updated May 31 2016 *)
CROSSREFS
AUTHOR
Alois P. Heinz, Sep 22 2008
STATUS
approved