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

0,2

Links

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

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 *)

Crossrefs

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

Sequence in context: A226996 A370247 A370273 * A340987 A186758 A262910

Adjacent sequences: A309952 A309953 A309954 * A309956 A309957 A309958

Keyword

nonn

Author

Alois P. Heinz, Aug 24 2019

Status

approved