A309955 a(n) = [x^n] (1 + p(x))^n, where p(x) is the g.f. of A000040.

1, 2, 10, 59, 362, 2287, 14707, 95762, 629386, 4166627, 27743445, 185602188, 1246543559, 8399791922, 56762121398, 384513835219, 2610322687850, 17753944125159, 120954505004605, 825274753259894, 5638438272353597, 38569743775323134, 264127692090124488

Offset: 0

Author

Alois P. Heinz, Aug 24 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1185

Crossrefs

Cf. A000040, A008485, A008578, A025174, A292871, A309950, A340990.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i=1, ithprime(n),
      (h-> add(b(j, h)*b(n-j, i-h), j=0..n))(iquo(i, 2))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..31);

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i == 1, Prime[n],
     Function[h, Sum[b[j, h]*b[n-j, i-h], {j, 0, n}]][Quotient[i, 2]]]];
a[n_] := b[n, n];
Table[a[n], {n, 0, 31}] (* Jean-François Alcover, Mar 19 2022, after Alois P. Heinz *)