A384454 -id:A384454 - cp's OEIS frontend

A015027 q-factorial numbers for q=-12.

1, 1, -11, -1463, 2333485, 44665236385, -10259202810507035, -28277368892180867021255, 935288538953861649874525071325, 371221802129246962654056875248358359825, -1768082733073463162105209099485375242162416580075, -101053866980328304416804100016021966697144304636338865493975

Offset: 0

Olivier Gérard

Vincenzo Librandi, Table of n, a(n) for n = 0..40
Index entries for sequences related to factorial numbers.

Column k=12 of A384454.

[1] cat [n le 1 select 1 else ((-12)^n - 1)*Self(n-1)/(-13): n in [1..13]]; // Vincenzo Librandi, Oct 26 2012

RecurrenceTable[{a[1]==1, a[n]==(((-12)^n - 1) * a[n-1])/(-13)}, a, {n, 15}] (* Vincenzo Librandi, Oct 26 2012 *)

a(n) = Product_{k=1..n} (q^k - 1) / (q - 1) for q=-12.
a(0) = 1, a(n) = ((-12)^n -1)*a(n-1)/(-13). - Vincenzo Librandi, Oct 26 2012
a(n) ~ (-1)^floor(n/2) * c * 12^(n*(n+1)/2) / 13^n, where c = Product_{k>=1} (1 - 1/(-12)^k) = 1.07638484220489190916... . - Amiram Eldar, Aug 10 2025

a(0)=1 prepended by Seiichi Manyama, May 31 2025

A015028 q-factorial numbers for q=-13.

Original entry on oeis.org

1, 1, -12, -1884, 3843360, 101929750560, -35142523960072320, -157510092662430660915840, 9177558663913662855639573043200, 6951672507594336724476921764731548211200, -68453363408439970530162052940526993784438155878400, -8762814767092584880014595182992133840006733019391100715212800

Offset: 0

Olivier Gérard

Vincenzo Librandi, Table of n, a(n) for n = 0..40
Index entries for sequences related to factorial numbers.

Column k=13 of A384454.

[1] cat [n le 1 select 1 else ((-13)^n - 1)*Self(n-1)/(-14): n in [1..13]]; // Vincenzo Librandi, Oct 26 2012

RecurrenceTable[{a[1]==1, a[n]==(((-13)^n - 1) a[n-1])/(-14)}, a, {n, 15}] (* Vincenzo Librandi, Oct 26 2012 *)

a(n) = Product_{k=1..n} ((-13)^k - 1) / (-13 - 1).
a(0) = 1, a(n) = ((-13)^n - 1)*a(n-1)/(-14). - Vincenzo Librandi, Oct 26 2012
a(n) ~ (-1)^floor(n/2) * c * 13^(n*(n+1)/2) / 14^n, where c = Product_{k>=1} (1 - 1/(-13)^k) = 1.07100320793234536419... . - Amiram Eldar, Aug 10 2025

a(0)=1 prepended by Seiichi Manyama, May 31 2025

A384453 a(n) is the n-th q-factorial number for q=-n.

Original entry on oeis.org

1, 1, -1, -14, 1989, 4551456, -212333070125, -246183190158589200, 8363069275661695069900425, 9589835030046843645163231485460480, -420238291486760860506028808179511473194550689, -785971734280677729025139143429963192709390305509012000000

Offset: 0

Seiichi Manyama, May 30 2025

sign

Index entries for sequences related to factorial numbers.

Main diagonal of A384454.

Cf. A347611.

Table[QFactorial[n, -n], {n, 0, 11}] (* Amiram Eldar, Aug 10 2025 *)

PARI
```
a(n) = prod(k=1, n, (1-(-n)^k)/(1+n));
```

a(n) = Product_{k=1..n} (1 - (-n)^k)/(1 + n).

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A015027 q-factorial numbers for q=-12.

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A015028 q-factorial numbers for q=-13.

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Author

Keywords

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Crossrefs

Programs

Magma

Mathematica

Formula

Extensions

A384453 a(n) is the n-th q-factorial number for q=-n.

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Author

Keywords

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Mathematica

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