A229807 G.f. satisfies: A(x) = x*exp( Sum_{n>=1} A(sigma(n)*x^n) / n ).

1, 1, 3, 7, 22, 53, 189, 485, 1688, 4689, 16650, 47187, 165262, 485268, 1728805, 5174302, 18049100, 55269365, 194672136, 603386084, 2099060047, 6614696429, 23137388920, 73539215187, 254877900451, 819954155438, 2849069767691, 9230855030167, 31891296634949, 104243641176924

Offset

1,3

Comments

Compare to: G(x) = x*exp( Sum_{n>=1} G(x^n)/n ), which is the g.f. of A000081, the number of rooted trees with n nodes.

Compare to: exp( Sum_{n>=1} sigma(n)*x^n/n ) = Product_{n>=1} 1/(1-x^n), which is the g.f. of the partition numbers (A000041).

Links

Table of n, a(n) for n=1..30.

Example

G.f.: A(x) = x + x^2 + 3*x^3 + 7*x^4 + 22*x^5 + 53*x^6 + 189*x^7 + 485*x^8 + ...
where
A(x) = x*exp(A(x) + A(3*x^2)/2 + A(4*x^3)/3 + A(7*x^4)/4 + A(6*x^5)/5 + A(12*x^6)/6 + A(8*x^7)/7 + A(15*x^8)/8 + A(13*x^9)/9 + A(18*x^10)/10 + ...).

Prog

(PARI) {a(n)=local(A=x); for(i=1, n, A=x*exp(sum(k=1, n, subst(A, x, sigma(k)*x^k +x*O(x^n))/k))); polcoeff(A, n)}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Cf. A000203 (sigma), A229900, A229901.

Sequence in context: A128599 A182174 A080882 * A229900 A079120 A092566

Adjacent sequences: A229804 A229805 A229806 * A229808 A229809 A229810

Keyword

nonn

Author

Paul D. Hanna, Oct 02 2013

Status

approved