

A160254


Expansion of x*(2  3*x + x^2  4*x^3 + 3*x^4  2*x^5 + x*(1  x  x^3)*sqrt((1 + 2*x)/(1  2*x)))/(2*(1  3*x + 3*x^2  3*x^3 + 4*x^4  3*x^5 + 2*x^6)).


1



1, 2, 4, 7, 13, 24, 44, 81, 151, 280, 525, 984, 1859, 3511, 6682, 12709, 24334, 46565, 89626, 172381, 333262, 643733, 1249147, 2421592, 4713715, 9165792, 17888456, 34873456, 68212220, 133269997, 261167821, 511211652, 1003436520, 1967293902
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OFFSET

1,2


COMMENTS

a(n) is the number of nodes at level n in certain generating tree, denoted C, that embeds the tree of numerical semigroups.
Elizalde (2009) established that the number A007323(n) of numerical semigroups of genus n is bounded in C as follows: A000045(n+2)  1 <= A007323(n) <= a(n) <= 1 + 3*2^(n  3).


LINKS

Matthew House, Table of n, a(n) for n = 1..3328
Sergi Elizalde, Improved bounds on the number of numerical semigroups of a given genus, arXiv:0905.0489 [math.CO], May 4, 2009. See Table 1, p. 8.


PROG

(Maxima) gf : taylor(x*(2  3*x + x^2  4*x^3 + 3*x^4  2*x^5 + x*(1  x  x^3)*sqrt((1 + 2*x)/(1  2*x)))/(2*(1  3*x + 3*x^2  3*x^3 + 4*x^4  3*x^5 + 2*x^6)), x, 0, 100)$
makelist(ratcoef(gf, x, n), n, 1, 100); /* Franck Maminirina Ramaharo, Jan 15 2019 */


CROSSREFS

Cf. A000045, A007323.
Sequence in context: A305442 A000073 A255069 * A276661 A005318 A102111
Adjacent sequences: A160251 A160252 A160253 * A160255 A160256 A160257


KEYWORD

nonn,easy


AUTHOR

Jonathan Vos Post, May 06 2009


EXTENSIONS

Edited, and name replaced by the g.f. by Franck Maminirina Ramaharo, Jan 15 2019


STATUS

approved



