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A261000 Unordered even-degree bilabelled increasing trees on 2n+1 nodes. 2
1, 3, 189, 68607, 82908441, 251944606683, 1618221395188629, 19514714407120367127, 405452689572115086887601, 13596354857453497541480646963, 699110237190377161907394095173869, 52888313306236766686682435536884784047 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..11.

Markus Kuba and Alois Panholzer, Combinatorial families of multilabelled increasing trees and hook-length formulas, arXiv:1411.4587 [math.CO], 2014. See p. 18

FORMULA

Kuba et al. (2014) gives a recurrence (see Theorem 7).

a(n) = A258659(2*n). - Michael Somos, Jun 17 2017

MAPLE

A261000aer := proc(n)

option remember;

local a, nloc, j, k, l;

if n = 1 then

1;

else

nloc := n-2 ;

a :=0 ;

for j from 0 to nloc-1 do

for k from 0 to nloc-1-j do

l := nloc-1-j-k ;

if l >= 0 then

a := a+procname(j+1)*procname(k+1)*procname(l+1) * (2*nloc+1)!/(2*j+1)!/(2*k+1)!/(2*l+1)! ;

end if;

end do:

end do:

%/2 ;

end if;

end proc:

A261000 := proc(n)

A261000aer(2*n+1) ;

end proc:

seq(A261000(n), n=0..15) ; # R. J. Mathar, Aug 18 2015

MATHEMATICA

terms = 12; nmax = 4 terms; A = 1; Do[A = Exp[Integrate[A^(1/2)*Integrate[1/A^(3/2), x], x] + O[x]^nmax], nmax]; A258659 = CoefficientList[A, x^2]*Range[0, nmax - 2, 2]!;

a[n_] := A258659[[2 n + 1]];

Table[a[n], {n, 0, terms - 1}] (* Jean-François Alcover, Nov 27 2017 *)

a[ n_] := If[ n<0, 0, (-1)^n * (4*n+1)! * SeriesCoefficient[ JacobiSD[x, 1/2], {x, 0, 4*n+1}]]; (* Michael Somos, Sep 03 2022 *)

PROG

(PARI) {a(n) = if( n<0, 0, my(m = 4*n + 1); m! * polcoeff( serreverse( intformal( 1 / sqrt(1 + x^4/4 + x * O(x^m)) ) ), m))}; /* Michael Somos, Jun 17 2017 */

CROSSREFS

Closely related to A104203.

Cf. A258659.

Sequence in context: A157236 A058856 A158469 * A032594 A159658 A257038

Adjacent sequences: A260997 A260998 A260999 * A261001 A261002 A261003

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Aug 09 2015

STATUS

approved

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Last modified February 3 01:16 EST 2023. Contains 360024 sequences. (Running on oeis4.)