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A101600 G.f.: c(3x)^2, c(x) the g.f. of A000108. 4
1, 6, 45, 378, 3402, 32076, 312741, 3127410, 31899582, 330595668, 3471254514, 36848701764, 394807518900, 4263921204120, 46370143094805, 507343918566690, 5580783104233590, 61682339573108100, 684673969261499910 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..18.

Samuele Giraudo, Pluriassociative algebras II: The polydendriform operad and related operads, arXiv:1603.01394 [math.CO], 2016.

FORMULA

G.f.: 4/(1+sqrt(1-12*x))^2.

a(n) = 3^n * A000108(n+1).

(n+2)*a(n) -6*(2*n+1)*a(n-1)=0. - R. J. Mathar, Nov 15 2011

O.g.f. A(x) = 1/x*series reversion( x/(1 + 3*x)^2 ). 1 + x*A'(x)/A(x) = 1/sqrt(1 - 12*x) is the o.g.f. for A098658. - Peter Bala, Jul 17 2015

MAPLE

Z[0]:=1: for k to 30 do Z[k]:=simplify(1/(1-3*z*Z[k-1])) od: g:=sum((Z[j]-Z[j-1]), j=1..30): gser:=series(g, z=0, 27): seq(coeff(gser, z, n)/3, n=1..19); # Zerinvary Lajos, May 21 2008

CROSSREFS

Cf. A050159, A101601, A101602, A098658.

Sequence in context: A153399 A007194 A025551 * A233668 A243694 A227169

Adjacent sequences:  A101597 A101598 A101599 * A101601 A101602 A101603

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Dec 08 2004

STATUS

approved

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Last modified September 20 10:51 EDT 2021. Contains 347584 sequences. (Running on oeis4.)