A227377 Limit of rows, when read in reverse, of triangle A227372.

1, 2, 4, 9, 14, 27, 46, 71, 113, 185, 280, 409, 614, 899, 1325, 1892, 2639, 3717, 5216, 7221, 9990, 13600, 18315, 24705, 33190, 44338, 58998, 78151, 102492, 133963, 174840, 227180, 294463, 380480, 489606, 628157, 801699, 1019864, 1295760, 1641900, 2074523

Offset

0,2

Comments

The g.f. of triangle A227372 satisfies: G(x,q) = 1 + x*G(q*x,q)*G(x,q)^2.

What is the generating function for this sequence?

Links

Table of n, a(n) for n=0..40.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 18*x^4 + 59*x^5 + 199*x^6 + 693*x^7 +...

Prog

(PARI) /* G.f. of A227372: G(x, q) = 1 + x*G(q*x, q)*G(x, q)^2: */
{A227372(n, k)=local(G=1); for(i=1, n, G=1+x*subst(G, x, q*x)*G^2 +x*O(x^n)); polcoeff(polcoeff(G, n, x), k, q)}
{a(n)=A227372(n+1, n*(n-1)/2)}
for(n=0, 40, print1(a(n), ", "))

Crossrefs

Cf. A227372, A227373.

Sequence in context: A169762 A291465 A355606 * A341959 A173407 A113862

Adjacent sequences: A227374 A227375 A227376 * A227378 A227379 A227380

Keyword

nonn

Author

Paul D. Hanna, Jul 10 2013

Status

approved