cp's OEIS Frontend

A309950 G.f.: Product_{j>=1} (1 + p(x^j)), where p(x) is the g.f. of A000040.

%I A309950 #19 Sep 15 2022 04:08:35
%S A309950 1,2,5,11,22,43,78,140,238,405,665,1077,1710,2685,4140,6336,9551,
%T A309950 14280,21117,30994,45051,65046,93170,132600,187439,263449,367999,
%U A309950 511409,706833,972257,1330929,1813846,2461090,3325803,4476276,6002036,8018216,10674307,14161656
%N A309950 G.f.: Product_{j>=1} (1 + p(x^j)), where p(x) is the g.f. of A000040.
%H A309950 Alois P. Heinz, <a href="/A309950/b309950.txt">Table of n, a(n) for n = 0..10000</a>
%p A309950 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i=1, ithprime(n),
%p A309950       add(b(j, 1)*(t-> b(t, min(t, i-1)))(n-i*j), j=0..n/i)))
%p A309950     end:
%p A309950 a:= n-> b(n$2):
%p A309950 seq(a(n), n=0..40);
%t A309950 b[n_, i_] := b[n, i] = If[n==0, 1, If[i==1,
%t A309950    Prime[n], Sum[b[j, 1]*Function[t,
%t A309950    b[t, Min[t, i-1]]][n-i*j], {j, 0, n/i}]]];
%t A309950 a[n_] := b[n, n];
%t A309950 Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Sep 15 2022, after _Alois P. Heinz_ *)
%Y A309950 Cf. A000040, A006171, A008578, A162891, A309955.
%K A309950 nonn
%O A309950 0,2
%A A309950 _Alois P. Heinz_, Aug 24 2019