A199543 G.f.: A(x) = Sum_{n>=0} x^n * A(x)^(n*(n+1)/2) * (1 - A(x)^(n+1))/(1 - A(x)).

1, 2, 9, 59, 462, 4011, 37253, 362877, 3662590, 38001809, 403118473, 4354812135, 47769686769, 530912871966, 5968147436150, 67766781921248, 776407323511627, 8967754230210974, 104351087348892229, 1222602680134075216, 14416253295843685409, 171018068867340738997

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Example

G.f.: A(x) = 1 + 2*x + 9*x^2 + 59*x^3 + 462*x^4 + 4011*x^5 + 37253*x^6 +...
where the g.f. A = A(x) satisfies the equivalent expressions:
A = 1 + x*A*(1-A^2)/(1-A) + x^2*A^3*(1-A^3)/(1-A) + x^3*A^6*(1-A^4)/(1-A) + x^4*A^10*(1-A^5)/(1-A) + x^5*A^15*(1-A^6)/(1-A) +...
A = 1 + x*(A + A^2) + x^2*(A^3 + A^4 + A^5) + x^3*(A^6 + A^7 + A^8 + A^9) + x^4*(A^10 + A^11 + A^12 + A^13 + A^14) +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, x^m*A^(m*(m+1)/2)*sum(k=0, m, A^k)+x*O(x^n))); polcoeff(A, n)}

Crossrefs

Cf. A199544, A199410.

Sequence in context: A184355 A346519 A151616 * A009636 A156272 A366240

Adjacent sequences: A199540 A199541 A199542 * A199544 A199545 A199546

Keyword

nonn

Author

Paul D. Hanna, Nov 07 2011

Status

approved