A195392 -id:A195392 - cp's OEIS frontend

A381162 a(n) = (8n)!/((n!)^4(4*n)!).

1, 1680, 32432400, 999456057600, 37905932634570000, 1617318175088527591680, 74451445170005824874553600, 3614146643656788883257309696000, 182458061523203642337177421198794000, 9493111901274733909567003010522405280000, 505860213332178847817809654781948251947782400

Offset: 0

Stefano Spezia, Feb 15 2025

nonn

Calabi-Yau series number 7.

S. Hassani, J.-M. Maillard, and N. Zenine, On the diagonals of rational functions: the minimal number of variables (unabridged version), arXiv:2502.05543 [math-ph], 2025. See pp. 14-15.

Cf. A100733, A134375, A195392.

Cf. A381161, A381163, A381164, A381165.

a[n_]:=(8n)!/((n!)^4*(4n)!); Array[a,11,0]

G.f.: hypergeom([1/8, 3/8, 5/8, 7/8], [1, 1, 1], 2^16*x).

a(n) ~ 2^(16*n - 3/2) / (Pi^2*n^2). - Vaclav Kotesovec, May 29 2025

A195393 a(n) = (9*n)!.

Original entry on oeis.org

1, 362880, 6402373705728000, 10888869450418352160768000000, 371993326789901217467999448150835200000000, 119622220865480194561963161495657715064383733760000000000

Offset: 0

Vincenzo Librandi, Sep 24 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..50

Cf. A000152, A010050, A100732, A100733, A100734, A195390, A195391, A195392.

Magma
```
[Factorial(9*n): n in [0..10]];
```

(9Range[0,10])! (* Harvey P. Dale, Jan 25 2023 *)

A195394 a(n) = (10*n)!

Original entry on oeis.org

1, 3628800, 2432902008176640000, 265252859812191058636308480000000, 815915283247897734345611269596115894272000000000, 30414093201713378043612608166064768844377641568960512000000000000

Offset: 0

Vincenzo Librandi, Sep 24 2011

Cf. A000142, A008592, A010050, A100732, A100733, A100734, A195390, A195391, A195392, A195393.

Cf. A195070, A196498.

Magma
```
[Factorial(10*n): n in [0..10]];
```

a[n_] := (10*n)!; Array[a, 6, 0] (* Amiram Eldar, Apr 03 2021 *)
(10*Range[0,10])! (* Harvey P. Dale, Aug 04 2025 *)

From Amiram Eldar, Apr 03 2021: (Start)
a(n) = A000142(A008592(n)).
Sum_{n>=0} 1/a(n) = A195070.
Sum_{n>=0} (-1)^n/a(n) = A196498. (End)

cp's OEIS Frontend

A381162 a(n) = (8n)!/((n!)^4(4*n)!).

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A195393 a(n) = (9*n)!.

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Author

Keywords

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Magma

Mathematica

A195394 a(n) = (10*n)!

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Author

Keywords

Crossrefs

Programs

Magma

Mathematica

Formula

cp's OEIS Frontend

A381162 a(n) = (8*n)!/((n!)^4*(4*n)!).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A195393 a(n) = (9*n)!.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

A195394 a(n) = (10*n)!

Views

Author

Keywords

Crossrefs

Programs

Magma

Mathematica

Formula

A381162 a(n) = (8n)!/((n!)^4(4*n)!).