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A124541 G.f.: A(x) = R_2(x)/R_1(x), where R_2(x) and R_1(x) are the g.f.s of row 2 (A124542) and row 1 (A124531), respectively, of table A124540. 0
1, 1, 4, 15, 63, 295, 1502, 8167, 46873, 281672, 1761798, 11418480, 76415644, 526594846, 3728435747, 27073765165, 201325681384, 1531247489953, 11899881220174, 94409837555587, 764105555574024, 6304959856949278 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

In table A124540, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = [ Sum_{k>=0} y^k*R_k(y)^n ]^n for n>=0.

LINKS

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

EXAMPLE

G.f.: A(x) = R_2(x)/R_1(x), where row g.f.s are:

R_2(x) = 1 + 2x + 7x^2 + 26x^3 + 107x^4 + 486x^5 + 2398x^6 +... and

R_1(x) = 1 + x + 2x^2 + 5x^3 + 16x^4 + 62x^5 + 274x^6 +..., so that

A(x) = 1 + x + 4*x^2 + 15*x^3 + 63*x^4 + 295*x^5 + 1502*x^6 +...

PROG

(PARI) {a(n)=local(R); R=vector(n+3, r, vector(n+3, c, 1)); for(i=0, n+2, for(r=0, n+2, R[r+1]=Vec(sum(c=0, n, x^c*Ser(R[c+1])^(r*c)+O(x^(n+1)))))); Vec(Ser(R[3])^2/Ser(R[2])+O(x^(n+1)))[n+1]}

CROSSREFS

Cf. A124540 (table); rows: A124531, A124542, A124543, A124544, A124545, A124546.

Sequence in context: A007167 A036728 A027216 * A323789 A007526 A233536

Adjacent sequences:  A124538 A124539 A124540 * A124542 A124543 A124544

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Nov 05 2006

STATUS

approved

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Last modified January 19 18:13 EST 2020. Contains 331051 sequences. (Running on oeis4.)