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A227377 Limit of rows, when read in reverse, of triangle A227372. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A119637 A169762 A291465 * A173407 A113862 A244624

Adjacent sequences:  A227374 A227375 A227376 * A227378 A227379 A227380

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 10 2013

STATUS

approved

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Last modified March 28 20:01 EDT 2020. Contains 333103 sequences. (Running on oeis4.)