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A249927 G.f. A(x) satisfies: 1+x = 2*A(x)^3 - A(x)^5. 6
1, 1, 4, 40, 485, 6585, 95732, 1457636, 22947585, 370494965, 6101028934, 102074877086, 1730213141683, 29649526507055, 512810063004600, 8940267160930408, 156944360941491106, 2771866193105829798, 49218079130561578390, 878107603236732844610, 15733529061871743649380 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..20.

FORMULA

G.f.: 1 + Series_Reversion(x - 4*x^2 - 8*x^3 - 5*x^4 - x^5).

EXAMPLE

G.f.: A(x) = 1 + x + 4*x^2 + 40*x^3 + 485*x^4 + 6585*x^5 + 95732*x^6 +...

Related expansions.

A(x)^3 = 1 + 3*x + 15*x^2 + 145*x^3 + 1755*x^4 + 23793*x^5 +...

A(x)^5 = 1 + 5*x + 30*x^2 + 290*x^3 + 3510*x^4 + 47586*x^5 +...

where 1+x = 2*A(x)^3 - A(x)^5.

PROG

(PARI) /* From 1+x = 2*A(x)^3 - A(x)^5: */

{a(n)=local(A=[1, 1]); for(i=1, n, A=concat(A, 0); A[#A]=-Vec(2*Ser(A)^3-Ser(A)^5)[#A]); A[n+1]}

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

(PARI) /* From Series Reversion: */

{a(n)=local(A=1+serreverse(x - 4*x^2 - 8*x^3 - 5*x^4 - x^5 + x^2*O(x^n))); polcoeff(A, n)}

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

CROSSREFS

Cf. A249926, A249928, A249929, A249930, A249931, A249932.

Sequence in context: A002705 A235372 A034385 * A218302 A296100 A214553

Adjacent sequences:  A249924 A249925 A249926 * A249928 A249929 A249930

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 27 2014

STATUS

approved

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Last modified June 26 00:12 EDT 2022. Contains 354870 sequences. (Running on oeis4.)