A363542 G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * (2^k + A(x^k)) * x^k/k ).

1, 3, 5, 14, 38, 114, 360, 1166, 3872, 13094, 44961, 156244, 548636, 1943333, 6935817, 24917586, 90039163, 327029681, 1193258619, 4371901789, 16077606949, 59325057056, 219579151797, 815017718383, 3032959638204, 11313632991360, 42295634914403

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Formula

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

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).

Prog

(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);

Crossrefs

Cf. A038075, A363543.

Cf. A362389.

Sequence in context: A052974 A284415 A318227 * A230585 A006395 A078718

Adjacent sequences: A363539 A363540 A363541 * A363543 A363544 A363545

Keyword

nonn

Author

Seiichi Manyama, Jun 09 2023

Status

approved