A295467 - OEIS

%I #12 Feb 21 2026 09:09:39

%S 1,45045,9704539845,2437781614596900,651257537955459119685,

%T 179888173423256639605246920,50740927694468549286238961648100,

%U 14520123213959375344187178875204676660,4199008318481460680983513774150641241683525,1224055446916973458193847787407419946733555964400

%N a(n) = (15*n)!*n!/((8*n)!*(5*n)!*(3*n)!).

%F G.f.: hypergeom([1/15, 2/15, 4/15, 7/15, 8/15, 11/15, 13/15, 14/15], [1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8], 5189853515625/16777216*x).

%F a(n) = binomial(15*n,7*n)*binomial(7*n,2*n)/binomial(3*n,n) = binomial(15*n,7*n)*binomial(8*n,3*n)/binomial(8*n,n). - _Chai Wah Wu_, Feb 16 2026

%F a(n) ~ 3^(12*n) * 5^(10*n) / (2^(24*n+2) * sqrt(Pi*n)). - _Amiram Eldar_, Feb 21 2026

%t a[n_] := (15*n)!*n!/((8*n)!*(5*n)!*(3*n)!); Array[a, 10, 0] (* _Amiram Eldar_, Feb 21 2026 *)

%o (Python)

%o from math import comb

%o def A295467(n): return comb(15*n,7*n)*comb(7*n,2*n)//comb(3*n,n) # _Chai Wah Wu_, Feb 16 2026

%Y Cf. A295431.

%K nonn,easy

%O 0,2

%A _Gheorghe Coserea_, Nov 28 2017