A363507 - OEIS

%I #14 Jun 07 2023 09:45:14

%S 1,4,14,50,191,763,3180,13640,59937,268304,1219626,5614038,26117296,

%T 122598622,579977691,2762264225,13234003724,63737225733,308406648979,

%U 1498558628584,7309116199687,35772044402485,175621484712091,864670723348447

%N G.f. satisfies A(x) = exp( Sum_{k>=1} (3 + A(x^k)) * x^k/k ).

%H Seiichi Manyama, <a href="/A363507/b363507.txt">Table of n, a(n) for n = 0..1000</a>

%F A(x) = Sum_{k>=0} a(k) * x^k = 1/(1-x)^3 * 1/Product_{k>=0} (1-x^(k+1))^a(k).

%F a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( 3 + Sum_{d|k} d * a(d-1) ) * a(n-k).

%o (PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (3+subst(A, x, x^k))*x^k/k)+x*O(x^n))); Vec(A);

%Y Cf. A000081, A029857, A036249, A363508.

%Y Cf. A363509.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jun 06 2023