OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1281
FORMULA
a(n) = [x^(2n)] (Sum_{j>=1} tau(j)*x^j)^n.
a(n) = A320019(2n,n).
MAPLE
b:= proc(n, k) option remember; `if`(k=0, 1,
`if`(k=1, numtheory[tau](n+1), (q->
add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..23);
MATHEMATICA
T[n_, k_] := T[n, k] = If[k == 0, If[n == 0, 1, 0], If[k == 1, If[n == 0, 0, DivisorSigma[0, n]], With[{q = Quotient[k, 2]}, Sum[T[j, q]*T[n - j, k - q], {j, 0, n}]]]];
a[n_] := T[2n, n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 01 2021
STATUS
approved