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A212072 G.f. satisfies: A(x) = (1 + x*A(x)^2)^3. 6
1, 3, 21, 190, 1950, 21576, 250971, 3025308, 37456650, 473498025, 6085977381, 79296104784, 1044955576496, 13903071489300, 186507160795350, 2519857658331576, 34258270557555282, 468322722628414290, 6433538749783033350, 88767899653496377050, 1229626632793564911906 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

a(n) = 3*binomial(6*n+3,n)/(6*n+3).

G.f. A(x) = G(x)^3 where G(x) = 1 + x*G(x)^6 is the g.f. of A002295.

EXAMPLE

G.f.: A(x) = 1 + 3*x + 21*x^2 + 190*x^3 + 1950*x^4 + 21576*x^5 +...

Related expansions:

A(x)^2 = 1 + 6*x + 51*x^2 + 506*x^3 + 5481*x^4 +...+ A002295(n+1)*x^n +...

A(x)^(1/3) = 1 + x + 6*x^2 + 51*x^3 + 506*x^4 +...+ A002295(n)*x^n +...

PROG

(PARI) {a(n)=binomial(6*n+3, n) * 3/(6*n+3)}

for(n=0, 40, print1(a(n), ", "))

(PARI) {a(n)=local(A=1+3*x); for(i=1, n, A=(1+x*A^2)^3+x*O(x^n)); polcoeff(A, n)}

CROSSREFS

Cf. A002295, A212071, A212073, A130564.

Sequence in context: A059863 A256625 A057616 * A212029 A219535 A292361

Adjacent sequences:  A212069 A212070 A212071 * A212073 A212074 A212075

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Apr 29 2012

STATUS

approved

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Last modified November 20 13:02 EST 2019. Contains 329336 sequences. (Running on oeis4.)