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%I #19 Mar 19 2022 12:45:13
%S 1,2,10,59,362,2287,14707,95762,629386,4166627,27743445,185602188,
%T 1246543559,8399791922,56762121398,384513835219,2610322687850,
%U 17753944125159,120954505004605,825274753259894,5638438272353597,38569743775323134,264127692090124488
%N a(n) = [x^n] (1 + p(x))^n, where p(x) is the g.f. of A000040.
%H Alois P. Heinz, <a href="/A309955/b309955.txt">Table of n, a(n) for n = 0..1185</a>
%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i=1, ithprime(n),
%p (h-> add(b(j, h)*b(n-j, i-h), j=0..n))(iquo(i, 2))))
%p end:
%p a:= n-> b(n$2):
%p seq(a(n), n=0..31);
%t b[n_, i_] := b[n, i] = If[n == 0, 1, If[i == 1, Prime[n],
%t Function[h, Sum[b[j, h]*b[n-j, i-h], {j, 0, n}]][Quotient[i, 2]]]];
%t a[n_] := b[n, n];
%t Table[a[n], {n, 0, 31}] (* _Jean-François Alcover_, Mar 19 2022, after _Alois P. Heinz_ *)
%Y Cf. A000040, A008485, A008578, A025174, A292871, A309950, A340990.
%K nonn
%O 0,2
%A _Alois P. Heinz_, Aug 24 2019
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