The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A357793

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A357793

a(n) = coefficient of x^n in A(x) = Sum_{n>=0} x^n*F(x)^n * (1 - x^n*F(x)^n)^n, where F(x) = 1 + x*F(x)^3 is a g.f. of A001764.
(history; published version)

#15 by Vaclav Kotesovec at Tue Mar 14 04:56:55 EDT 2023

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editing

approved

#14 by Vaclav Kotesovec at Tue Mar 14 04:56:37 EDT 2023

FORMULA

a(n) ~ c * 3^(3*n) / (n^(3/2) * 2^(2*n)), where c = 0.0403028056146458801802487899052088995113692232406693619.... - Vaclav Kotesovec, Mar 14 2023

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approved

editing

#13 by Paul D. Hanna at Sat Dec 24 04:25:39 EST 2022

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approved

#12 by Paul D. Hanna at Sat Dec 24 04:25:37 EST 2022

EXAMPLE

The radius of convergence of the power series A(x) equals 4/27.

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approved

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#11 by Paul D. Hanna at Sat Dec 24 04:16:03 EST 2022

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editing

approved

#10 by Paul D. Hanna at Sat Dec 24 04:15:46 EST 2022

EXAMPLE

SPECIFIC VALUES.

The radius of convergence equals 4/27.

The power series A(x) converges at x = 4/27 to

A(4/27) = 1.2311920996301390036800654138630946234233891541082821783156...

which equals the following sums:

(1) A(4/27) = Sum_{n>=0} 2^n * (9^n - 2^n)^n / 9^(n*(n+1)),

(2) A(4/27) = Sum_{n>=1} (-1)^(n-1) * 2^(n*(n-1)) * 9^n / (9^n - 2^n)^n.

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approved

editing

#9 by N. J. A. Sloane at Wed Dec 21 20:18:24 EST 2022

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proposed

approved

#8 by Paul D. Hanna at Wed Dec 21 07:28:30 EST 2022

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editing

proposed

#7 by Paul D. Hanna at Wed Dec 21 07:28:28 EST 2022

FORMULA

Given F(x) = 1 + x*F(x)^3, g.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies may be defined by the following.

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proposed

editing

#6 by Paul D. Hanna at Tue Dec 20 17:03:39 EST 2022

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editing

proposed