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A171190 G.f. satisfies: A(x) = exp( Sum_{n>=1} [A(x)^n + A(-x)^n]*x^n/n ). 2
1, 2, 3, 10, 27, 112, 336, 1490, 4791, 22138, 74079, 351288, 1207620, 5831208, 20436516, 100004994, 355610367, 1758044950, 6322608561, 31511387450, 114359284515, 573713781760, 2097612975456, 10580600244664, 38925304968612 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..24.

FORMULA

G.f. satisfies: A(x) = 1/[(1 - x*A(x))*(1 - x*A(-x))]. - Paul D. Hanna, Dec 06 2009

EXAMPLE

G.f.: A(x) = 1 + 2*x + 3*x^2 + 10*x^3 + 27*x^4 + 112*x^5 + 336*x^6 + ...

log(A(x)) = [A(x)+A(-x)]*x + [A(x)^2+A(-x)^2]*x^2/2 + [A(x)^3+A(-x)^3]*x^3/3 + ...

PROG

(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=exp(sum(m=1, n, (A^m+subst(A^m, x, -x)+x*O(x^n))*x^m/m))); polcoeff(A, n)}

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=(1-x*A+x*O(x^n))^-1*(1-x*subst(A, x, -x)+x*O(x^n))^-1); polcoeff(A, n)} \\ Paul D. Hanna, Dec 06 2009

CROSSREFS

Cf. A171191, A171199.

Sequence in context: A089752 A264759 A323680 * A216332 A007029 A298083

Adjacent sequences:  A171187 A171188 A171189 * A171191 A171192 A171193

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 05 2009

STATUS

approved

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Last modified August 9 05:12 EDT 2020. Contains 336319 sequences. (Running on oeis4.)