|
Search: id:A102410
|
|
|
| A102410 |
|
Odd triangle n!. This table read by rows gives the coefficients of sum formulae of n-th Factorials (A000142). The k-th row (6>=k>=1) contains T(i,k) for i=1 to k+2, where k=[2*n+3+(-1)^n]/4 and T(i,k) satisfies n! = Sum_{i=1..k+2} T(i,k) * n^(i-1) / (2*k-2)!. |
|
+0
4
|
|
| 1, 0, 0, -6, 3, 1, 0, 2400, -2024, 264, 32, 0, 2570400, 909720, -666540, 55800, 3420, 0, -19071521280, 12195884736, -762499920, -282106440, 22425480, 741384, 840, -219303218534400, -11953192930560, 27128332828800, -2808016545600, -125442525600, 14164990560, 280576800
(list; table; graph; listen)
|
|
|
OFFSET
|
1,4
|
|
|
COMMENT
|
Incidently, the sum of signed coefficients for each k-th row is divisible by (2*k-2)!.
|
|
LINKS
|
A. F. Labossiere, Sobalian Coefficients.
A. F. Labossiere, Miscellaneous.
|
|
EXAMPLE
|
11!=39916800; substituting n=11 in the formula of the k-th row we obtain k=6
and the coefficients T(i,6) are those needed for computing 11!.
=> 11! = [ -219303218534400 -11953192930560*11 +27128332828800*11^2 -2808016545600*11^3
-125442525600*11^4 +14164990560*11^5 +280576800*11^6 +453600*11^7 ]/10! = 39916800.
|
|
CROSSREFS
|
Cf. A102409, A008276, A094216, A000142, A094638, A101751, A102411, A102412, A101752, A003422, A101559, A101032, A099731.
Sequence in context: A153459 A102525 A119923 this_sequence A105123 A058291 A132615
Adjacent sequences: A102407 A102408 A102409 this_sequence A102411 A102412 A102413
|
|
KEYWORD
|
sign,tabl,uned
|
|
AUTHOR
|
Andre F. Labossiere (boronali(AT)laposte.net), Jan 07 2005
|
|
|
Search completed in 0.002 seconds
|
