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A001716 Generalized Stirling numbers.
(Formerly M4651 N1990)
+0
7
1, 9, 74, 638, 5944, 60216, 662640, 7893840, 101378880, 1397759040, 20606463360, 323626665600, 5395972377600, 95218662067200, 1773217155225600, 34758188233574400, 715437948072960000, 15429680577561600000 (list; graph; listen)
OFFSET

0,2

COMMENT

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 20 2009: (Start)

The asymptotic expansion of the higher order exponential integral E(x,m=2,n=4) ~ exp(-x)/x^2*(1 - 9/x + 74/x^2 - 638/x^3 + 5944/x^4 - 60216/x^5 + 662640/x^6 - ... ) leads to the sequence given above. See A163931 and A028421 for more information.

(End)

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).

FORMULA

a(n) = sum((-1)^(n+k)*(k+1)*4^k*stirling1(n+1, k+1), k=0..n). - Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004

a(n)=n!*sum((-1)^k*binomial(-4,k)/(n-k),k=0..n-1); [From Milan R. Janjic (agnus(AT)blic.net), Dec 14 2008]

CROSSREFS

Sequence in context: A075232 A145524 A037533 this_sequence A028991 A102094 A125397

Adjacent sequences: A001713 A001714 A001715 this_sequence A001717 A001718 A001719

KEYWORD

nonn

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

More terms from Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


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