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A324152
a(0)=1; for n>0, a(n) = (3/((n+1)*(n+2)*(n+3))) * multinomial(4*n;n,n,n,n).
4
1, 3, 126, 9240, 900900, 104756652, 13742520792, 1968826448160, 301700280152700, 48756255150603000, 8226155369009738160, 1438285479229504301760, 259131100507849025033760, 47897087290614993606462000, 9050997011303368719799740000
OFFSET
0,2
It is conjectured that a(n) is always an integer.
If all terms except the first are doubled, we get A324478, which IS known to be integral.
Luis Fredes, Avelio Sepulveda, Tree-decorated planar maps, arXiv:1901.04981 [math.CO], 2019. See Remark 4.6.
FORMULA
a(n+1) = a(n)*4*(4*n+1)*(4*n+2)*(4*n+3)/((n+1)^2*(n+4)) for n>0.
From Vaclav Kotesovec, Jul 21 2019: (Start)
For n>0, a(n) = 3*(4*n)! / ((n!)^3 * (n+3)!).
a(n) ~ 3 * 2^(8*n - 1/2) / (Pi^(3/2) * n^(9/2)). (End)
MATHEMATICA
c[m_, n_] := m Product[1/(n + i), {i, m}] (Multinomial @@ ConstantArray[n, m + 1]); {1}~Join~Array[c[3, #] &, 14] (* Michael De Vlieger, Mar 01 2019 *)
Flatten[{1, Table[3*(4*n)! / ((n!)^3 * (n+3)!), {n, 1, 15}]}] (* Vaclav Kotesovec, Jul 21 2019 *)
PROG
(Magma) [1] cat [n le 1 select 3 else Self(n-1)*4*(4*n-3)*(4*n-2)*(4*n-1)/((n)^2*(n+3)): n in [1..20]]; // Vincenzo Librandi, Mar 11 2019
CROSSREFS
Cf. A000108, A324151, A324465 (exponent of 2), A324467, A324478.
Sequence in context: A157547 A160879 A157562 * A274314 A157592 A213988
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified September 19 23:07 EDT 2024. Contains 376015 sequences. (Running on oeis4.)