A219230 G.f.: exp( Sum_{n>=1} x^n/n * Product_{k>=1} 1/(1 - x^(n*k)*(1 + x^n)^k) ).

1, 1, 2, 5, 13, 32, 82, 201, 498, 1214, 2954, 7117, 17115, 40880, 97336, 230699, 545068, 1283150, 3011783, 7047353, 16445814, 38275172, 88859213, 205796476, 475539242, 1096428621, 2522704211, 5792637135, 13275381694, 30367439045, 69341077367, 158059717986, 359688534284

Offset

0,3

Comments

Compare to the dual g.f. of A218575:

exp( Sum_{n>=1} x^n/n * Product_{k>=1} 1/(1 - x^(n*k)*(1 + x^k)^n) ).

Links

Paul D. Hanna, Table of n, a(n) for n = 0..1000

Example

G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 13*x^4 + 32*x^5 + 82*x^6 + 201*x^7 +...
where
log(A(x)) = x/(1*(1-x*(1+x))*(1-x^2*(1+x)^2)*(1-x^3*(1+x)^3)*...) +
x^2/(2*(1-x^2*(1+x^2))*(1-x^4*(1+x^2)^2)*(1-x^6*(1+x^2)^3)*...) +
x^3/(3*(1-x^3*(1+x^3))*(1-x^6*(1+x^3)^2)*(1-x^9*(1+x^3)^3)*...) +
x^4/(4*(1-x^4*(1+x^4))*(1-x^8*(1+x^4)^2)*(1-x^12*(1+x^4)^3)*...) +...
Explicitly,
log(A(x)) = x + 3*x^2/2 + 10*x^3/3 + 31*x^4/4 + 81*x^5/5 + 228*x^6/6 + 554*x^7/7 + 1399*x^8/8 + 3313*x^9/9 + 7843*x^10/10 +...

Prog

(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, x^m/m*prod(k=1, n\m, 1/(1-x^(m*k)*(1+x^m)^k +x*O(x^n))))), n)}
for(n=0, 40, print1(a(n), ", "))

Crossrefs

Cf. A218575, A219229, A219232.

Sequence in context: A255630 A298535 A110320 * A108890 A220739 A337282

Adjacent sequences: A219227 A219228 A219229 * A219231 A219232 A219233

Keyword

nonn

Author

Paul D. Hanna, Nov 15 2012

Status

approved