numbpart(n, {a = k})

["Ruud H.G. van Tol" <rvtol@isolution.nl>]

For https://oeis.org/A046682, I created this code:

first(nn) = {
  my( v = Vec( 1 / prod( k=1, nn, 1+(-x)^k, 1+x*O(x^nn) ) ) );
  vector( nn, i, ( numbpart(i-1) + v[i] ) / 2 );
}

This takes about a minute to return 10k values.

Is there a faster way to initialize v?

Would a variant numbpart(n, {a = k}) be interesting, like Maple has?
With the optional a-parameter like with partitions(k, {a = k}, {n = k}).

-- Greetings, Ruud