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A188662
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Binomial coefficients: a(n) = binomial(3*n,n)^2.
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16
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1, 9, 225, 7056, 245025, 9018009, 344622096, 13521038400, 540917591841, 21966328580625, 902702926350225, 37456461988358400, 1566697064677290000, 65973795093338597136, 2794203818390077646400, 118933541228935777741056, 5084343623375056062840609
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OFFSET
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0,2
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COMMENTS
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Even-order terms in the diagonal of rational function 1/(1 - (x^2 + y^2 + z^2 - x*y - y*z - x*z)). - Gheorghe Coserea, Aug 09 2018
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LINKS
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FORMULA
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a(n) = binomial(3*n,n)^2 = ( [x^n](1 + x)^(3*n) )^2 = [x^n](F(x)^(9*n)), where F(x) = 1 + x + 4*x^2 + 49*x^3 + 795*x^4 + 15180*x^5 + 320422*x^6 + ... appears to have integer coefficients. For similar results see A000897, A002894, A002897, A006480, A008977 and A186420. - Peter Bala, Jul 12 2016
a(n) = Sum_{k=0..n} binomial(n, k)^2*binomial(3*n+k, 2*n). - Seiichi Manyama, Jan 09 2017
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MATHEMATICA
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Table[Binomial[3 n, n]^2, {n, 0, 16}]
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PROG
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(Maxima) makelist(binomial(3*n, n)^2, n, 0, 16);
(Python)
from math import comb
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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