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URL: https://oeis.org/A295437

⇱ A295437 - OEIS

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A295437
a(n) = (18*n)!*n!/((9*n)!*(6*n)!*(4*n)!).
4
1, 1021020, 6016814703900, 41477110789150966020, 304331361887290342345862940, 2309513382640863232775760738593520, 17900786683992090777583802478540374204100, 140773522690118901080808611014971776285838687000
OFFSET
0,2
FORMULA
G.f.: hypergeom([1/18, 5/18, 7/18, 11/18, 13/18, 17/18], [1/4, 1/3, 1/2, 2/3, 3/4], 8503056*x).
a(n) ~ 2^(4*n - 3/2) * 3^(12*n - 1/2) / sqrt(Pi*n). - Vaclav Kotesovec, Jul 11 2025
a(n) = binomial(18*n,9*n)*binomial(9*n,3*n)/binomial(4*n,n) = binomial(18*n,9*n)*binomial(10*n,4*n)/binomial(10*n,n). - Chai Wah Wu, Feb 15 2026
MATHEMATICA
Array[(18 #)!*#!/((9 #)!*(6 #)!*(4 #)!) &, 8, 0] (* Michael De Vlieger, Nov 23 2017 *)
CoefficientList[ Series[ HypergeometricPFQ[{1/18, 5/18, 7/18, 11/18, 13/18, 17/18}, {1/4, 1/3, 1/2, 2/3, 3/4}, 8503056 x], {x, 0, 8}], x] (* Robert G. Wilson v, Nov 23 2017 *)
PROG
(Python)
from math import comb
def A295437(n): return comb(18*n, 9*n)*comb(9*n, 3*n)//comb(4*n, n) # Chai Wah Wu, Feb 15 2026
CROSSREFS
Cf. A295431.
Sequence in context: A232144 A293127 A190381 * A254265 A254258 A254304
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Nov 23 2017
STATUS
approved