The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A290957

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A290957

G.f. A(x) satisfies: A( 2*A(x)^2 - 4*A(x)^3 ) = 2*x^2 + 4*x^3.
(history; published version)

#20 by Vaclav Kotesovec at Mon Aug 28 07:35:25 EDT 2017

STATUS

editing

approved

#19 by Vaclav Kotesovec at Mon Aug 28 07:35:19 EDT 2017

FORMULA

a(n) ~ c * d^n / n^(3/2), where d = 5.6107024438745823... and c = 0.07583382126393587... - Vaclav Kotesovec, Aug 28 2017

STATUS

approved

editing

#18 by Paul D. Hanna at Mon Aug 14 22:53:23 EDT 2017

STATUS

editing

approved

#17 by Paul D. Hanna at Mon Aug 14 22:52:18 EDT 2017

NAME

G.f. A(x) satisfies: A( 2*A(x)^2 - 4*A(x)^3 ) = 2*x^2 + 4*x^3.

EXAMPLE

Related series begin:

2*A(x)^2 - 4*A(x)^3 = 2*x^2 - 12*x^3 + 56*x^4 - 272*x^5 + 1312*x^6 - 6432*x^7 + 32640*x^8 - 170576*x^9 + 911696*x^10 - 4963760*x^11 + 27425200*x^12 +...

2*B(x)^2 + 4*B(x)^3 = 2*x^2 + 12*x^3 + 40*x^4 + 112*x^5 + 416*x^6 + 2112*x^7 + 10336*x^8 + 45936*x^9 + 206192*x^10 + 999376*x^11 + 5026640*x^12 +...

STATUS

approved

editing

#16 by Paul D. Hanna at Mon Aug 14 22:43:34 EDT 2017

STATUS

editing

approved

#15 by Paul D. Hanna at Mon Aug 14 22:43:30 EDT 2017

EXAMPLE

Let B(x) be the series reversion of A(x), then B(x) is the g.f. of A290958 and B(x) begins;

STATUS

approved

editing

#14 by Paul D. Hanna at Mon Aug 14 22:39:23 EDT 2017

STATUS

editing

approved

#13 by Paul D. Hanna at Mon Aug 14 22:39:20 EDT 2017

COMMENTS

Series reversion of the g.f. is described by A290958.

STATUS

approved

editing

#12 by Paul D. Hanna at Mon Aug 14 22:35:43 EDT 2017

STATUS

editing

approved

#11 by Paul D. Hanna at Mon Aug 14 22:35:39 EDT 2017

EXAMPLE

G.f.: A(x) = x + 2*x^2 + 2*x^3 + 6*x^4 + 40*x^5 + 208*x^6 + 798*x^7 + 3122*x^8 + 15038*x^9 + 77830*x^10 + 381798*x^11 + 1819998*x^12 + 8925172*x^13 + 45280900*x^14 + 231030138*x^15 + 1171823534*x^16 + 5962836408*x^17 + 30668699312*x^18 + 158951012362*x^19 + 825830001086*x^20 +...

STATUS

approved

editing