This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A049460 Generalized Stirling number triangle of first kind. 8
 1, -5, 1, 30, -11, 1, -210, 107, -18, 1, 1680, -1066, 251, -26, 1, -15120, 11274, -3325, 485, -35, 1, 151200, -127860, 44524, -8175, 835, -45, 1, -1663200, 1557660, -617624, 134449, -17360, 1330, -56, 1, 19958400, -20355120 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n,m)= ^5P_n^m in the notation of the given reference with a(0,0) := 1. The monic row polynomials s(n,x) := sum(a(n,m)*x^m,m=0..n) which are s(n,x)= product(x-(5+k),k=0..n-1), n >= 1 and s(0,x)=1 satisfy s(n,x+y) = sum(binomial(n,k)*s(k,x)*S1(n-k,y),k=0..n), with the Stirling1 polynomials S1(n,x)=sum(A008275(n,m)*x^m, m=1..n) and S1(0,x)=1. In the umbral calculus (see the S. Roman reference given in A048854) the s(n,x) polynomials are called Sheffer for (exp(5*t),exp(t)-1). 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 Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened FORMULA a(n, m)= a(n-1, m-1) - (n+4)*a(n-1, m), n >= m >= 0; a(n, m) := 0, n    (zipWith (-) ([0] ++ row) \$ map (* i) (row ++ [0]), i + 1)) ([1], 5) -- Reinhard Zumkeller, Mar 11 2014 CROSSREFS Unsigned column sequences are: A001720-A001724. Row sums (signed triangle): A001715(n+3)*(-1)^n. Row sums (unsigned triangle): A001725(n+5). Cf. A000035 A084938. Sequence in context: A144890 A144891 A135892 * A145926 A062140 A144355 Adjacent sequences:  A049457 A049458 A049459 * A049461 A049462 A049463 KEYWORD sign,easy,tabl AUTHOR EXTENSIONS Second formula corrected by Philippe Deléham, Nov 10 2008 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.

Last modified October 23 20:01 EDT 2019. Contains 328373 sequences. (Running on oeis4.)