A363579 -id:A363579 - cp's OEIS frontend

A363581 G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * x^k/(k * (1 + 3*x^k)) ).

1, 1, -1, 4, -6, 11, -22, 62, -151, 353, -867, 2261, -5861, 15178, -39878, 106099, -283823, 763248, -2065453, 5621318, -15368682, 42190539, -116281176, 321647511, -892617214, 2484583934, -6935203356, 19408586888, -54447145335, 153084848495

Offset: 0

Seiichi Manyama, Jun 10 2023

sign

Cf. A052855, A198518, A363545, A363546, A363580.

Cf. A363579.

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

A(x) = (1 + 3*x) * B(x) where B(x) is the g.f. of A363579.

a(n) = A363579(n) + 3*A363579(n-1) for n > 0.

A363578 G.f. satisfies A(x) = exp( Sum_{k>=1} ((-2)^k + A(x^k)) * x^k/k ).

Original entry on oeis.org

1, -1, 2, -2, 4, -6, 13, -20, 38, -65, 129, -228, 435, -794, 1528, -2833, 5421, -10189, 19561, -37091, 71247, -135973, 261879, -502303, 969181, -1866210, 3608664, -6970576, 13504298, -26152744, 50758711, -98515611, 191517618, -372404560, 725061378

Offset: 0

Seiichi Manyama, Jun 10 2023

sign

Cf. A001678, A036249, A362389, A363541, A363579.

Cf. A363580.

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);

A(x) = B(x)/(1 + 2*x) where B(x) is the g.f. of A363580.
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).

cp's OEIS Frontend

A363581 G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * x^k/(k * (1 + 3*x^k)) ).

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula