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A001701 Generalized Stirling numbers.
(Formerly M4169 N1735)
19
1, 6, 26, 71, 155, 295, 511, 826, 1266, 1860, 2640, 3641, 4901, 6461, 8365, 10660, 13396, 16626, 20406, 24795, 29855, 35651, 42251, 49726, 58150, 67600, 78156, 89901, 102921, 117305, 133145, 150536, 169576, 190366, 213010, 237615, 264291, 293151, 324311 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

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

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

Robert E. Moritz, On the sum of products of n consecutive integers, Univ. Washington Publications in Math., 1 (No. 3, 1926), 44-49 [Annotated scanned copy]

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

a(n) = n(n-1)(3n^2+17n+26)/24, n>1.

G.f.: x-x*(6-4*x+x^2) ) / (x-1)^5. - Simon Plouffe in his 1992 dissertation.

If we define f(n,i,a)=sum(binomial(n,k)*stirling1(n-k,i)*product(-a-j,j=0..k-1),k=0..n-i), then a(n) = f(n,n-2,2), for n>=2. [From Milan Janjic, Dec 20 2008]

MAPLE

A001701 := proc(n)

    if n = 1 then

        1;

    else

        n*(n-1)*(3*n^2+17*n+26)/24 ;

    end if;

end proc: # R. J. Mathar, Sep 23 2016

MATHEMATICA

f[k_] := k + 1; t[n_] := Table[f[k], {k, 1, n}]; a[n_] := SymmetricPolynomial[2, t[n]]; Table[a[n], {n, 2, 30}] (* Clark Kimberling, Dec 31 2011 *)

CROSSREFS

Equals A059302(n+2) + 1, n>1. Partial sums of A005564.

Sequence in context: A190095 A135036 A166796 * A241452 A175898 A255870

Adjacent sequences:  A001698 A001699 A001700 * A001702 A001703 A001704

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 21 14:29 EST 2018. Contains 299414 sequences. (Running on oeis4.)