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A213282 G.f. satisfies: A(x) = G(x/(1-x)^3) where G(x) = 1 + x*G(x)^3 is the g.f. of A001764. 3
1, 1, 6, 36, 236, 1656, 12192, 92960, 727824, 5817696, 47281472, 389533056, 3245867136, 27308274688, 231654031104, 1979205694464, 17016094611712, 147104972637696, 1277988764697600, 11151534242977792, 97692088569096192, 858890594909048832, 7575804347863105536 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Compare to the g.f. B(x) of A006319 where B(x) = C(x/(1-x)^2) such that C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers (A000108).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

G.f. satisfies: A(x) = F(x*A(x)^3) where F(x) = 1 + x/F(-x)^3 is the g.f. of A213281.

G.f. A(x) satisfies: A(1 - G(-x)) = G(x) = 1 + x*G(x)^3 is the g.f. of A001764.

EXAMPLE

G.f.: A(x) = 1 + x + 6*x^2 + 36*x^3 + 236*x^4 + 1656*x^5 + 12192*x^6 +...

G.f.: A(x) = G(x/(1-x)^3) where G(x) = 1 + x*G(x)^3 is g.f. of A001764:

G(x) = 1 + x + 3*x^2 + 12*x^3 + 55*x^4 + 273*x^5 + 1428*x^6 +...

MAPLE

series(RootOf(G = 1 + G^3*x/(1-x)^3, G), x=0, 30); # Mark van Hoeij, Apr 18 2013

PROG

(PARI) /* G.f. A(x) = G(x/(1-x)^3) where G(x) = 1 + x*G(x)^3: */

{a(n)=local(A, G=1+x); for(i=1, n, G=1+x*G^3+x*O(x^n)); A=subst(G, x, x/(1-x+x*O(x^n))^3); polcoeff(A, n)}

for(n=0, 25, print1(a(n), ", "))

(PARI) /* G.f. A(x) = F(x*A(x)^3) where F(x) = 1 + x/F(-x)^3: */

{a(n)=local(F=1+x+x*O(x^n), A=1); for(i=1, n+1, F=1+x/subst(F^3, x, -x+x*O(x^n))); A=(serreverse(x/F^3)/x)^(1/3); polcoeff(A, n)}

for(n=0, 25, print1(a(n), ", "))

CROSSREFS

Cf. A213281, A001764; variants: A006319 (royal paths in a lattice), A213336.

Sequence in context: A099252 A057395 A259819 * A066053 A153824 A001286

Adjacent sequences:  A213279 A213280 A213281 * A213283 A213284 A213285

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 08 2012

STATUS

approved

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Last modified April 8 08:54 EDT 2020. Contains 333313 sequences. (Running on oeis4.)