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A143916 G.f. A(x) satisfies: A(x) = 1+x + x^2*A(x)*A'(x). 5
1, 1, 1, 3, 12, 62, 385, 2781, 22848, 210176, 2139336, 23872450, 289825228, 3803859030, 53676793157, 810508456373, 13041332257860, 222776899815744, 4026846590787586, 76792054455516582, 1540845309830989064 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..445

FORMULA

a(n) ~ c * n!, where constant c = A238214 / exp(1) = 0.669014536209527303065690569951975534726... - Vaclav Kotesovec, Feb 21 2014

a(0) = 1, a(1) = 1, a(n) = Sum_{0 < k < n} k * a(k) * a(n-k-1). - Vladimir Reshetnikov, May 17 2016

EXAMPLE

G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 12*x^4 + 62*x^5 + 385*x^6 +...

A'(x) = 1 + 2*x + 9*x^2 + 48*x^3 + 310*x^4 + 2310*x^5 + 19467*x^6 +...

A(x)*A'(x) = 1 + 3*x + 12*x^2 + 62*x^3 + 385*x^4 + 2781*x^5 +...

MATHEMATICA

a[0] = 1; a[1] = 1; a[n_] := a[n] = Sum[k a[k] a[n-k-1], {k, 1, n-1}]; Table[a[n], {n, 0, 20}] (* Vladimir Reshetnikov, May 17 2016 *)

PROG

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

CROSSREFS

Cf. A143917 (variant), A238214.

Sequence in context: A045740 A187820 A074529 * A323630 A020033 A266329

Adjacent sequences:  A143913 A143914 A143915 * A143917 A143918 A143919

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 05 2008

STATUS

approved

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Last modified January 26 23:05 EST 2020. Contains 331289 sequences. (Running on oeis4.)