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

0,2

Links

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

Formula

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).

Prog

(PARI) 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);

Crossrefs

Cf. A000081, A179469, A363440.

Cf. A363423.

Sequence in context: A169604 A081341 A355353 * A132900 A050623 A037760

Adjacent sequences: A363436 A363437 A363438 * A363440 A363441 A363442

Keyword

nonn

Author

Seiichi Manyama, Jun 02 2023

Status

approved