A362389 G.f. satisfies A(x) = exp( Sum_{k>=1} (2^k + A(x^k)) * x^k/k ).

1, 3, 10, 34, 122, 450, 1723, 6758, 27135, 110913, 460395, 1935233, 8222504, 35255000, 152353021, 662892684, 2901595559, 12768195617, 56450822365, 250637657015, 1117060889815, 4995815027658, 22413020866875, 100842092305575, 454912716037387

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

A(x) = B(x)/(1 - 2*x) where B(x) is the g.f. of A363545.

A(x) = Sum_{k>=0} a(k) * x^k = 1/(1-2*x) * 1/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} d * a(d-1) ) * a(n-k).

Prog

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

Crossrefs

Cf. A001678, A036249, A363541.

Cf. A029857, A363542, A363545.

Sequence in context: A026616 A306409 A047032 * A149032 A149033 A149034

Adjacent sequences: A362386 A362387 A362388 * A362390 A362391 A362392

Keyword

nonn

Author

Seiichi Manyama, Jun 09 2023

Status

approved