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A085687 G.f.: 8/(1+sqrt(1-8*x))^3. 2
1, 6, 36, 224, 1440, 9504, 64064, 439296, 3055104, 21498880, 152807424, 1095450624, 7911587840, 57511157760, 420459724800, 3089600348160, 22806128885760, 169033661153280, 1257467341701120, 9385880636620800, 70271680244613120, 527595313582571520 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is also the number of paths of length 2(n+1) in a binary tree between two vertices that are 2 steps apart. [From David Koslicki (koslicki(AT)math.psu.edu), Nov 02 2010]

LINKS

Table of n, a(n) for n=0..21.

FORMULA

6(n+1)*2^(n-2)*Cat(n+2)/(2n+3), where Cat(n)=A000108(n). - Ralf Stephan, Mar 11 2004

G.f.: c(2x)^3, where c(x) is the g.f. of A000108; a(n)=3(n+1)2^n*Cat(n+1)/(n+3); - Paul Barry, Dec 08 2004

D-finite with recurrence: (n+3)*a(n) -2*(5*n+7)*a(n-1) +8*(2*n-1)*a(n-2)=0. - R. J. Mathar, Nov 15 2011

CROSSREFS

Cf. A002421.

Sequence in context: A218991 A166748 A200378 * A242136 A129327 A244889

Adjacent sequences:  A085684 A085685 A085686 * A085688 A085689 A085690

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jul 13 2003

STATUS

approved

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Last modified May 16 11:33 EDT 2021. Contains 343942 sequences. (Running on oeis4.)