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A065866 n!* Catalan(n+1). 3
1, 2, 10, 84, 1008, 15840, 308880, 7207200, 196035840, 6094932480, 213322636800, 8303173401600, 355850288640000, 16653793508352000, 845180020548864000, 46236318771202560000, 2712530701243883520000, 169890080762116915200000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

R. L. Graham, D. E. Knuth, O. Patashnik, "Concrete Mathematics", Addison-Wesley, 1994, pp. 200-204.

LINKS

Harry J. Smith, Table of n, a(n) for n=0,...,100

FORMULA

a(n) = 2 * (2n+1)!/(n+2)!. E.g.f.: (1-2x-sqrt(1-4x))/(2x^2) = (O.g.f. for A000108)^2 = B_2(x)^2 (cf. GKP reference)

MAPLE

with(combstruct):ZL:=[T, {T=Union(Z, Prod(Epsilon, Z, T), Prod(T, Z, Epsilon), Prod(T, T, Z))}, labeled]:seq(count(ZL, size=i)/i, i=1..18); - Zerinvary Lajos, Dec 16 2007

PROG

(PARI) { for (n = 0, 100, a = 2 * (2*n + 1)!/(n + 2)!; write("b065866.txt", n, " ", a) ) } [From Harry J. Smith, Nov 02 2009]

CROSSREFS

Cf. A000108.

Equals 2 * A102693(n+1), n>0.

Sequence in context: A113332 A180715 A107863 * A156466 A132397 A202745

Adjacent sequences:  A065863 A065864 A065865 * A065867 A065868 A065869

KEYWORD

nonn

AUTHOR

Len Smiley (smiley(AT)math.uaa.alaska.edu), Dec 06 2001

STATUS

approved

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Last modified November 27 17:39 EST 2014. Contains 250249 sequences.