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A300282 E.g.f. A(x) satisfies: A'(x) = 1/(1 - A(A(x)))^2. 0
1, 2, 14, 176, 3256, 80464, 2508432, 94989088, 4253855744, 220832422912, 13086217711232, 874394085363328, 65223621800358400, 5386555341558256640, 489099399479737741824, 48537534403454393734656, 5237456183532299486332928, 611754844797595116933365760, 77043077295500803834985809920, 10424760435433013614451330201600 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..20.

FORMULA

E.g.f. A(x) satisfies:

(1) A(x) = Series_Reversion( Integral (1 - A(x))^2 dx ).

(2) A'(x) = 1 / (1 - A(A(x)))^2.

(3) A''(x) = 2 / ( (1 - A(A(x)))^5 * (1 - A(A(A(x))))^2 ).

EXAMPLE

G.f.: A(x) = x + 2*x^2/2! + 14*x^3/3! + 176*x^4/4! + 3256*x^5/5! + 80464*x^6/6! + 2508432*x^7/7! + 94989088*x^8/8! + 4253855744*x^9/9! + ...

such that A'(x) = 1/(1 - A(A(x)))^2.

RELATED SERIES.

(1 - A(x))^2 = 1 - 2*x - 2*x^2/2! - 16*x^3/3! - 216*x^4/4! - 4192*x^5/5! - 107376*x^6/6! - 3444384*x^7/7! - 133557568*x^8/8! - 6103032256*x^9/9! + ...

Series_Reversion(A(x)) = x - 2*x^2/2! - 2*x^3/3! - 16*x^4/4! - 216*x^5/5! - 4192*x^6/6! - 107376*x^7/7! + ...

A(A(x)) = x + 4*x^2/2! + 40*x^3/3! + 656*x^4/4! + 15152*x^5/5! + 455280*x^6/6! + 16947776*x^7/7! + 756120640*x^8/8! + 39475100864*x^9/9! + ...

PROG

(PARI) {a(n)=local(A=x, G); for(i=1, n, G = intformal( (1 - A +x*O(x^n))^2 ); A = serreverse(G)); n!*polcoeff(A, n)}

for(n=1, 25, print1(a(n), ", "))

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

for(n=1, 25, print1(a(n), ", "))

CROSSREFS

Cf. A210949.

Sequence in context: A308449 A233224 A167014 * A336635 A352761 A208195

Adjacent sequences:  A300279 A300280 A300281 * A300283 A300284 A300285

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Mar 07 2018

STATUS

approved

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Last modified October 1 09:13 EDT 2022. Contains 357140 sequences. (Running on oeis4.)