A363547 -id:A363547 - cp's OEIS frontend

A363548 G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * x^k/(k * (1 - x^k)^3) ).

1, 1, 5, 19, 79, 326, 1414, 6198, 27794, 126233, 580885, 2700135, 12665756, 59869222, 284919675, 1364009722, 6564545500, 31742029545, 154134718727, 751316355122, 3674923035139, 18031965040197, 88734141475113, 437813286219942, 2165445447313147

Offset: 0

Seiichi Manyama, Jun 09 2023

nonn

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

Cf. A052855, A363547.

Cf. A363507, A363546.

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

A(x) = (1 - x)^3 * B(x) where B(x) is the g.f. of A363507.

a(n) = Sum_{k=0..3} (-1)^k * binomial(3,k) * A363507(n-k).

A363567 G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * x^k/(k * (1 + x^k)^2) ).

Original entry on oeis.org

1, 1, 0, 1, 1, 0, 1, 2, 1, 1, 3, 3, 2, 4, 7, 7, 7, 12, 17, 17, 22, 37, 47, 51, 73, 110, 133, 162, 242, 339, 412, 545, 798, 1065, 1342, 1860, 2648, 3474, 4547, 6400, 8874, 11665, 15754, 22152, 30205, 40201, 55301, 77115, 104463, 141087, 195669, 270620, 366902

Offset: 0

Seiichi Manyama, Jun 10 2023

nonn

Cf. A198518, A363575.

Cf. A363547, A363565.

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

A(x) = (1 + x)^2 * B(x) where B(x) is the g.f. of A363565.

a(n) = Sum_{k=0..2} binomial(2,k) * A363565(n-k).

cp's OEIS Frontend

A363548 G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * x^k/(k * (1 - x^k)^3) ).

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