A363470 -id:A363470 - cp's OEIS frontend

A363471 G.f. satisfies A(x) = exp( 3 * Sum_{k>=1} A(-x^k) * x^k/k ).

1, 3, -3, -26, 48, 444, -920, -9126, 19587, 204214, -449496, -4841001, 10856283, 119585034, -271813440, -3044796399, 6991433415, 79341313335, -183641493481, -2105713558467, 4905239040894, 56722082044512, -132833292089826, -1546827734185557

Offset: 0

Seiichi Manyama, Jun 03 2023

sign

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

Cf. A006964, A200402, A363470.

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

A(x) = B(x)^3 where B(x) is the g.f. of A200402.
A(x) = Sum_{k>=0} a(k) * x^k = 1/Product_{k>=0} (1-x^(k+1))^(3 * (-1)^k * a(k)).
a(0) = 1; a(n) = (3/n) * Sum_{k=1..n} ( Sum_{d|k} d * (-1)^(d-1) * a(d-1) ) * a(n-k).

A363474 G.f. satisfies A(x) = exp( 2 * Sum_{k>=1} (-1)^(k+1) * A(-x^k) * x^k/k ).

Original entry on oeis.org

1, 2, -3, -14, 22, 138, -213, -1536, 2474, 18928, -31451, -248992, 420804, 3416514, -5844716, -48349920, 83503128, 700674606, -1219159874, -10345673158, 18109290380, 155082913608, -272798814028, -2353889042848, 4157686512816, 36104006239798

Offset: 0

Seiichi Manyama, Jun 03 2023

sign

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

Cf. A306768, A363475.

Cf. A005753, A363470.

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

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

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

cp's OEIS Frontend

A363471 G.f. satisfies A(x) = exp( 3 * Sum_{k>=1} A(-x^k) * x^k/k ).

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