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

Author

Paul D. Hanna, Jul 10 2013

Keywords

• nonn

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?

Examples

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

Crossrefs

Cf. A227372, A227373.

Programs

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),", "))