A221546 G.f.: Sum_{n>=0} x^n * (1+x)^(n^2) / (1 + x*(1+x)^n)^n.

1, 1, 1, 2, 5, 13, 46, 160, 658, 2867, 13481, 68123, 363995, 2059994, 12265480, 76553192, 499565710, 3397751507, 24030183367, 176345076712, 1340147071794, 10528875578996, 85382909823373, 713673454720854, 6140525989112831, 54321576239313034, 493542862587980827

Offset

0,4

Links

Paul D. Hanna, Table of n, a(n) for n = 0..520

Example

G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 5*x^4 + 13*x^5 + 46*x^6 + 160*x^7 +...
where
A(x) = 1 + x*(1+x)/(1 + x*(1+x)) + x^2*(1+x)^4/(1 + x*(1+x)^2)^2 + x^3*(1+x)^9/(1 + x*(1+x)^3)^3 + x^4*(1+x)^16/(1 + x*(1+x)^4)^4 +...

Prog

(PARI) {a(n)=polcoeff(sum(m=0, n, x^m*(1+x)^(m^2)/(1+x*(1+x)^m+x*O(x^n))^m), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A221547.

Sequence in context: A212830 A000719 A149875 * A085632 A111563 A079573

Adjacent sequences: A221543 A221544 A221545 * A221547 A221548 A221549

Keyword

nonn

Author

Paul D. Hanna, Jan 19 2013

Status

approved