A230352 G.f.: A(x) = x*exp( Sum_{n>=1} Sum_{d|n} A(d*x^n) / n ).

1, 1, 3, 7, 20, 49, 148, 391, 1167, 3309, 9974, 29083, 88851, 265815, 818676, 2497633, 7753214, 23968298, 75015661, 234347623, 738220718, 2325779822, 7369929088, 23374281968, 74451070741, 237439581606, 759696374373, 2434110886204, 7818771362163, 25150994589336, 81070450302439

Offset

1,3

Links

Table of n, a(n) for n=1..31.

Example

G.f.: A(x) = x + x^2 + 3*x^3 + 7*x^4 + 20*x^5 + 49*x^6 + 148*x^7 + 391*x^8 + ...
where
log(A(x)/x) = A(x) + (A(x^2) + A(2*x^2))/2 + (A(x^3) + A(3*x^3))/3 + (A(x^4) + A(2*x^4) + A(4*x^4))/4 + (A(x^5) + A(5*x^5))/5 + (A(x^6) + A(2*x^6) + A(3*x^6) + A(6*x^6))/6 + (A(x^7) + A(7*x^7))/7 + (A(x^8) + A(2*x^8) + A(4*x^8) + A(8*x^8))/8 + (A(x^9) + A(3*x^9) + A(9*x^9))/9 + ...

Mathematica

a[n_] := Module[{A=x}, For[i=1, i <= n, i++, A=x*Exp[Sum[DivisorSum[k, (A /. x :> #*x^k + x*O[x]^n)&]/k, {k, 1, n}]]]; SeriesCoefficient[A, n]]; Table[Print[an = a[n]]; an, {n, 1, 35}] (* Jean-François Alcover, Dec 10 2015, adapted from PARI *)

Prog

(PARI) {a(n)=local(A=x); for(i=1, n, A=x*exp(sum(k=1, n, sumdiv(k, d, subst(A, x, d*x^k +x*O(x^n)))/k))); polcoeff(A, n)}
for(n=1, 35, print1(a(n), ", "))

Crossrefs

Cf. A229807.

Sequence in context: A243100 A173400 A281971 * A271894 A066315 A339061

Adjacent sequences: A230349 A230350 A230351 * A230353 A230354 A230355

Keyword

nonn

Author

Paul D. Hanna, Oct 16 2013

Status

approved