login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A089503 Triangle of numbers used for basis change between certain falling factorials. 2
1, 1, 4, 1, 12, 30, 1, 24, 168, 336, 1, 40, 540, 2880, 5040, 1, 60, 1320, 13200, 59400, 95040, 1, 84, 2730, 43680, 360360, 1441440, 2162160, 1, 112, 5040, 117600, 1528800, 11007360, 40360320, 57657600, 1, 144, 8568, 274176, 5140800, 57576960 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Used to relate array A078739 ((2,2)-Stirling2) to triangle A071951 (Legendre-Stirling).

LINKS

Table of n, a(n) for n=1..42.

W. Lang, First 9 rows.

FORMULA

fallfac(x+n-1, 2*n) = sum(a(n, m)*fallfac(x, 2*n-(m-1)), m=1..n), n>=1 and with fallfac(x, k) := product(x+1-j, j=1..k), with fallfac(n, k)=A068424(n, k) (falling factorials). a(n, m)=0 if n < m.

EXAMPLE

The triangle begins:

n\m 1   2    3      4       5        6        7        8 ...

1:  1

2:  1   4

3:  1  12   30

4:  1  24  168    336

5:  1  40  540   2880    5040

6:  1  60 1320  13200   59400    95040

7:  1  84 2730  43680  360360  1441440  2162160

8:  1 112 5040 117600 1528800 11007360 40360320 57657600

...

Row 9:  1 144 8568 274176 5140800 57576960 374250240 1283143680 1764322560

Row 10: 1 180 13680 574560 14651280 234420480 2344204800 14065228800 45711993600 60949324800.

Reformatted - Wolfdieter Lang, Apr 10 2013

n=3: fallfac(x+2,6) = 1*fallfac(x,6) + 12*fallfac(x,5) + 30*fallfac(x,4).

MATHEMATICA

eq[n_, x_] := Sum[FactorialPower[x, 1 - m + 2*n]*a[n, m], {m, 1, n}] == FactorialPower[x + n - 1, 2*n]; eq[n_] := Table[eq[n, x], {x, n + 1, 2*n}]; row[n_] := First[Table[a[n, m], {m, 1, n}] /. Solve[eq[n]]]; Array[row, 10] // Flatten (* Jean-Fran├žois Alcover, Sep 02 2016 *)

CROSSREFS

Sequence in context: A105197 A157398 A306299 * A019236 A019237 A019238

Adjacent sequences:  A089500 A089501 A089502 * A089504 A089505 A089506

KEYWORD

nonn,easy,tabl

AUTHOR

Wolfdieter Lang, Dec 01 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 23 22:47 EDT 2019. Contains 325278 sequences. (Running on oeis4.)