A363471 -id:A363471 - cp's OEIS frontend

A363470 G.f. satisfies A(x) = exp( 2 * Sum_{k>=1} A(-x^k) * x^k/k ).

1, 2, -1, -6, 7, 42, -58, -366, 513, 3406, -4846, -33310, 48304, 339446, -499133, -3565468, 5294439, 38312242, -57332347, -419177900, 631252549, 4654229300, -7045498256, -52310262192, 79531957334, 593986308994, -906439292326, -6803984285256

Offset: 0

Seiichi Manyama, Jun 03 2023

sign

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

Cf. A000151, A200438, A363471.

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

A(x) = B(x)^2 where B(x) is the g.f. of A200438.
A(x) = Sum_{k>=0} a(k) * x^k = 1/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-1) * a(d-1) ) * a(n-k).

A363475 G.f. satisfies A(x) = exp( 3 * Sum_{k>=1} (-1)^(k+1) * A(-x^k) * x^k/k ).

Original entry on oeis.org

1, 3, -6, -44, 96, 918, -2073, -22278, 52629, 597627, -1451736, -17065641, 42205373, 508415817, -1273766637, -15623442097, 39528583206, 491601500847, -1253383246330, -15759867676416, 40430096479776, 512914242127868, -1322511998532891

Offset: 0

Seiichi Manyama, Jun 03 2023

sign

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

Cf. A306768, A363474.

Cf. A052757, A363471.

seq(n) = my(A=1); for(i=1, n, A=exp(3*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))^(3 * (-1)^k * a(k)).

a(0) = 1; a(n) = (3/n) * Sum_{k=1..n} ( Sum_{d|k} d * (-1)^(d+k/d) * a(d-1) ) * a(n-k).

cp's OEIS Frontend

A363470 G.f. satisfies A(x) = exp( 2 * Sum_{k>=1} A(-x^k) * x^k/k ).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula