VOOZH about

URL: https://oeis.org/A295432

⇱ A295432 - OEIS

login
A295432
a(n) = (12*n)!*(3*n)!*(2*n)!/((6*n)!*(6*n)!*(4*n)!*n!).
4
1, 462, 579462, 825012300, 1240292449350, 1922257130698212, 3037843525927941276, 4866407206411278522456, 7873830606510488097067590, 12837724391783995395083457780, 21058175422921386792478888300212, 34712605923460405627194955063564200
OFFSET
0,2
FORMULA
G.f.: hypergeom([1/12, 5/12, 7/12, 11/12], [1/6, 1/2, 5/6], 1728*x).
a(n) = a(n-1)*6*(12*n - 1)*(12*n - 5)*(12*n - 7)*(12*n - 11)/(n*(2*n - 1)*(6*n - 1)*(6*n - 5)). - Neven Sajko, Jul 22 2023
a(n) ~ 2^(6*n - 1) * 3^(3*n) / sqrt(Pi*n). - Vaclav Kotesovec, Jul 11 2025
a(n) = binomial(12*n,6*n)*binomial(2*n,n)/binomial(4*n,n) = binomial(12*n,6*n)*binomial(5*n,n)/binomial(5*n,2*n). - Chai Wah Wu, Feb 15 2026
MATHEMATICA
Array[(12 #)!*(3 #)!*(2 #)!/((6 #)!*(6 #)!*(4 #)!*#!) &, 12, 0] (* Michael De Vlieger, Nov 23 2017 *)
CoefficientList[ Series[ HypergeometricPFQ[{1/12, 5/12, 7/12, 11/12}, {1/6, 1/2, 5/6}, 1728 x], {x, 0, 11}], x] (* Robert G. Wilson v, Nov 23 2017 *)
PROG
(Python)
from math import comb
def A295432(n): return comb(12*n, 6*n)*comb(2*n, n)//comb(4*n, n) # Chai Wah Wu, Feb 15 2026
CROSSREFS
Cf. A295431.
Sequence in context: A208619 A318266 A383796 * A213406 A294853 A025038
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Nov 23 2017
STATUS
approved