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A126596 a(n) = binomial(4*n,n)*(2*n+1)/(3*n+1). 6
1, 3, 20, 154, 1260, 10659, 92092, 807300, 7152444, 63882940, 574221648, 5188082354, 47073334100, 428634152730, 3914819231400, 35848190542920, 329007937216860, 3025582795190340, 27872496751392496, 257172019222240200, 2376196095585231920, 21983235825545286435 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of standard Young tableaux of shape [3n,n].  Also the number of binary words with 3n 1's and n 0's such that for every prefix the number of 1's is >= the number of 0's.  The a(1) = 3 words are: 1011, 1101, 1110. - Alois P. Heinz, Aug 15 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..100

FORMULA

a(n) = A039599(2*n,n).

a(n) = (2*n+1)*A002293(n). - Mark van Hoeij, Nov 17 2011

a(n) = A208983(2*n+1). - Reinhard Zumkeller, Mar 04 2012

a(n) = A005810(n) * A005408(n) / A016777(n). - Reinhard Zumkeller, Mar 04 2012

a(n) = [x^n] ((1 - sqrt(1 - 4*x))/(2*x))^(2*n+1). - Ilya Gutkovskiy, Nov 01 2017

Recurrence: 3*n*(3*n-1)*(3*n+1)*a(n) = 8*(2*n+1)*(4*n-3)*(4*n-1)*a(n-1). - Vaclav Kotesovec, Feb 03 2018

MAPLE

seq((2*n+1)*binomial(4*n, n)/(3*n+1), n=0..22); # Emeric Deutsch, Mar 27 2007

MATHEMATICA

Table[(Binomial[4n, n](2n+1))/(3n+1), {n, 0, 30}] (* Harvey P. Dale, Feb 06 2016 *)

PROG

(MAGMA) [Binomial(4*n, n)*(2*n+1)/(3*n+1): n in [0..20]]; // Vincenzo Librandi, Nov 18 2011

(Haskell)

a126596 n = a005810 n * a005408 n `div` a016777 n

-- Reinhard Zumkeller, Mar 04 2012

CROSSREFS

Column k=3 of A214776.

Sequence in context: A154627 A091172 A091168 * A074560 A123355 A258791

Adjacent sequences:  A126593 A126594 A126595 * A126597 A126598 A126599

KEYWORD

nonn,easy

AUTHOR

Philippe Deléham, Mar 13 2007

EXTENSIONS

More terms from Emeric Deutsch, Mar 27 2007

STATUS

approved

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Last modified February 20 21:53 EST 2018. Contains 299387 sequences. (Running on oeis4.)