A363542 - OEIS

%I #10 Jun 09 2023 08:54:19

%S 1,3,5,14,38,114,360,1166,3872,13094,44961,156244,548636,1943333,

%T 6935817,24917586,90039163,327029681,1193258619,4371901789,

%U 16077606949,59325057056,219579151797,815017718383,3032959638204,11313632991360,42295634914403

%N G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * (2^k + A(x^k)) * x^k/k ).

%F A(x) = Sum_{k>=0} a(k) * x^k = (1+2*x) * Product_{k>=0} (1+x^(k+1))^a(k).

%F a(0) = 1; a(n) = (-1/n) * Sum_{k=1..n} ( (-2)^k + Sum_{d|k} (-1)^(k/d) * d * a(d-1) ) * a(n-k).

%o (PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (-1)^(k+1)*(2^k+subst(A, x, x^k))*x^k/k)+x*O(x^n))); Vec(A);

%Y Cf. A038075, A363543.

%Y Cf. A362389.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jun 09 2023