A363440 -id:A363440 - cp's OEIS frontend

A363439 G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * (3*x)^k/k ).

1, 3, 18, 108, 702, 4698, 32913, 236844, 1747170, 13131639, 100239444, 774932832, 6055105590, 47742847875, 379381851684, 3035174325246, 24426965179593, 197622494260479, 1606332527049645, 13111628672610153, 107428845309125157

Offset: 0

Seiichi Manyama, Jun 02 2023

nonn

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

Cf. A000081, A179469, A363440.

Cf. A363423.

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

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

A363443 G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^k) * (4*x)^k/k ).

Original entry on oeis.org

1, 4, 16, 128, 864, 6912, 55936, 470016, 4025600, 35144704, 311190784, 2789206016, 25254028288, 230652174336, 2122466561024, 19659305379840, 183146187440128, 1714933158969344, 16131631511164928, 152366562180972544

Offset: 0

Seiichi Manyama, Jun 02 2023

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..996

Cf. A004111, A363441, A363442.

Cf. A363427, A363440.

seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (-1)^(k+1)*subst(A, x, x^k)*(4*x)^k/k)+x*O(x^n))); Vec(A);

A(x) = Sum_{k>=0} a(k) * x^k = Product_{k>=0} (1+4*x^(k+1))^a(k).

a(0) = 1; a(n) = (-1/n) * Sum_{k=1..n} ( Sum_{d|k} d * (-4)^(k/d) * a(d-1) ) * a(n-k).

cp's OEIS Frontend

A363439 G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * (3*x)^k/k ).

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