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A088327 G.f.: exp(Sum_{k>=1} B(x^k)/k), where B(x) = x + 2*x^2 + 5*x^3 + 14*x^4 + 42*x^5 + ... = (C(x)-1)/x and C is the g.f. for the Catalan numbers A000108. 2
1, 1, 3, 8, 25, 77, 256, 854, 2940, 10229, 36124, 128745, 463137, 1677816, 6118165, 22432778, 82660369, 305916561, 1136621136, 4238006039, 15852603939, 59471304434, 223704813807, 843547443903, 3188064830876, 12074092672950, 45816941923597, 174173975322767 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) is the number of forests of rooted plane binary trees (each node has outdegree = 0 or 2) where the trees have a total of n internal nodes.  Cf. A222006. - Geoffrey Critzer, Feb 26 2013

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

Euler transform of Catalan numbers (A000108). - Franklin T. Adams-Watters, Mar 01 2006

MAPLE

with(numtheory):

a:= proc(n) option remember; `if`(n=0, 1, add(add(d*

       binomial(2*d, d)/(d+1), d=divisors(j))*a(n-j), j=1..n)/n)

    end:

seq(a(n), n=0..40);  # Alois P. Heinz, Sep 10 2012

MATHEMATICA

nn=20; CoefficientList[Series[Product[1/(1-x^i)^CatalanNumber[i], {i, 1, nn}], {x, 0, nn}], x] (* Geoffrey Critzer, Feb 26 2013 *).

CROSSREFS

Row sums of A275431.

Cf. A222006.

Sequence in context: A022553 A292884 A148789 * A148790 A148791 A148792

Adjacent sequences:  A088324 A088325 A088326 * A088328 A088329 A088330

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 06 2003

STATUS

approved

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Last modified February 23 05:44 EST 2018. Contains 299473 sequences. (Running on oeis4.)