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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A051231 Generalized Stirling number triangle of first kind. 2
1, -9, 1, 162, -27, 1, -4374, 891, -54, 1, 157464, -36450, 2835, -90, 1, -7085880, 1797714, -164025, 6885, -135, 1, 382637520, -104162436, 10655064, -535815, 14175, -189, 1, -24106163760, 6944870988, -775431468, 44411409, -1428840, 26082, -252, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n,m)= R_n^m(a=0,b=9) in the notation of the given reference.

a(n,m) is a Jabotinsky matrix, i.e., the monic row polynomials E(n,x) := sum(a(n,m)*x^m,m=1..n) = product(x-9*j,j=0..n-1), n >= 1, E(0,x) := 1, are exponential convolution polynomials (see A039692 for the definition and a Knuth reference).

REFERENCES

Mitrinovic, D. S.; Mitrinovic, R. S.; Tableaux d'une classe de nombres relies aux nombres de Stirling. Univ. Beograd. Pubi. Elektrotehn. Fak. Ser. Mat. Fiz. No. 77 1962, 77 pp.

LINKS

Table of n, a(n) for n=1..36.

FORMULA

a(n, m) = a(n-1, m-1) - 9*(n-1)*a(n-1, m), n >= m >= 1; a(n, m) := 0, n<m; a(n, 0) := 0, a(1, 1)=1. E.g.f. for m-th column of signed triangle: (((log(1+9*x))/9)^m)/m!.

EXAMPLE

{1}; {-9,1}; {162,-27,1}; {-4374,891,-54,1}; ... E(3,x) = 162*x-27*x^2+x^3.

CROSSREFS

First (m=1) column sequence is A051232(n-1). Row sums (signed triangle): A049211(n-1)*(-1)^(n-1). Row sums (unsigned triangle): A045756(n). Cf. A051187 (b=8 triangle).

Sequence in context: A243754 A254932 A223511 * A258437 A046761 A193373

Adjacent sequences:  A051228 A051229 A051230 * A051232 A051233 A051234

KEYWORD

sign,easy,tabl

AUTHOR

Wolfdieter Lang

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 January 21 11:47 EST 2019. Contains 319354 sequences. (Running on oeis4.)