A363443 -id:A363443 - cp's OEIS frontend

A363441 G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^k) * (2*x)^k/k ).

1, 2, 4, 16, 52, 208, 840, 3520, 15008, 65344, 288408, 1288416, 5813744, 26460800, 121333200, 559991712, 2599385536, 12127405952, 56837861376, 267473333120, 1263354463056, 5987210061184, 28461008374480, 135672151034304, 648406644570048

Offset: 0

Seiichi Manyama, Jun 02 2023

nonn

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

Cf. A004111, A363442, A363443.

Cf. A179469, A363425.

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

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

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

A363442 G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^k) * (3*x)^k/k ).

Original entry on oeis.org

1, 3, 9, 54, 270, 1620, 9828, 61884, 397062, 2597508, 17232831, 115722918, 784996434, 5371325217, 37029240315, 256948639344, 1793271890988, 12579466538187, 88645665923244, 627235978623318, 4454619888380355, 31743030458459169, 226890102674671245

Offset: 0

Seiichi Manyama, Jun 02 2023

nonn

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

Cf. A004111, A363441, A363443.

Cf. A363426, A363439.

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

A(x) = Sum_{k>=0} a(k) * x^k = Product_{k>=0} (1+3*x^(k+1))^a(k).

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

cp's OEIS Frontend

A363441 G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^k) * (2*x)^k/k ).

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