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A216493 G.f. satisfies: A(x) = 1 + x*A(x)^3 + x^5*A(x)^13. 1
1, 1, 3, 12, 55, 274, 1444, 7923, 44803, 259325, 1529008, 9151327, 55454164, 339543312, 2097460255, 13055579858, 81803671623, 515552408141, 3265924761595, 20784056808550, 132812937949820, 851847261569025, 5482066256568375, 35388168141000935, 229081418808206500, 1486757986305948780, 9672120691595571320 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..26.

FORMULA

G.f. satisfies: A(x) = 1/A(-x*A(x)^5); note that the g.f. of A001764, G(x) = 1 + x*G(x)^3, also satisfies this condition.

EXAMPLE

G.f.: A(x) = 1 + x + 3*x^2 + 12*x^3 + 55*x^4 + 274*x^5 + 1444*x^6 + 7923*x^7 +...

Related expansions:

A(x)^3 = 1 + 3*x + 12*x^2 + 55*x^3 + 273*x^4 + 1431*x^5 + 7806*x^6 + 43893*x^7 +...

A(x)^13 = 1 + 13*x + 117*x^2 + 910*x^3 + 6578*x^4 + 45643*x^5 + 309127*x^6 +...

Given (1) A(x) = 1 + x*A(x)^3 + x^5*A(x)^13,

suppose (2) A(x) = 1/A(-x*A(x)^5),

then substituting x in (1) with -x*A(x)^5 yields:

1/A(x) = 1 - x*A(x)^5/A(x)^3 - x^5*A(x)^25/A(x)^13,

which illustrates that (2) is consistent with (1).

PROG

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x*A^3+x^5*A^13 +x*O(x^n)); polcoeff(A, n)}

for(n=0, 30, print1(a(n), ", "))

CROSSREFS

Cf. A216494, A216490, A001764.

Sequence in context: A179848 A001764 A171780 * A216494 A120920 A179487

Adjacent sequences:  A216490 A216491 A216492 * A216494 A216495 A216496

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 07 2012

STATUS

approved

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Last modified February 17 17:27 EST 2018. Contains 299296 sequences. (Running on oeis4.)