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A001702 Generalized Stirling numbers.
(Formerly M5148 N2234)
2
1, 24, 154, 580, 1665, 4025, 8624, 16884, 30810, 53130, 87450, 138424, 211939, 315315, 457520, 649400, 903924, 1236444, 1664970, 2210460, 2897125, 3752749, 4809024, 6101900, 7671950, 9564750, 11831274, 14528304, 17718855, 21472615, 25866400, 30984624 (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.

FORMULA

a(n) = (1/48)*(n-1)*n*(n+1)*(n+4)*(n^2+7n+14), n>1.

G.f.: x +x^2*(x-4)*(x^2-2*x+6)/(x-1)^7 . - 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-1) = -f(n,n-3,2), for n>=3. [From Milan Janjic, Dec 20 2008]

MAPLE

A001702 := proc(n)

    if n = 1 then

        1 ;

    else

        (n-1)*n*(n+1)*(n+4)*(n^2+7*n+14)/48 ;

    end if;

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

MATHEMATICA

Join[{1}, Table[(n-1) n (n+1) (n+4) (n^2 + 7 n + 14)/48, {n, 2, 100}]] (* T. D. Noe, Aug 09 2012 *)

CROSSREFS

Sequence in context: A159650 A279459 A092181 * A004308 A008663 A277984

Adjacent sequences:  A001699 A001700 A001701 * A001703 A001704 A001705

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 25 04:05 EST 2018. Contains 299630 sequences. (Running on oeis4.)