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A001722 Generalized Stirling numbers.
(Formerly M5061 N2191)
2
1, 18, 251, 3325, 44524, 617624, 8969148, 136954044, 2201931576, 37272482280, 663644774880, 12413008539360, 243533741849280, 5003753991174720, 107497490419296000, 2410964056571616000, 56366432074677312000, 1371711629236971456000, 34699437370290760704000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The asymptotic expansion of the higher order exponential integral E(x,m=3,n=5) ~ exp(-x)/x^3*(1 - 18/x + 251/x^2 - 3325/x^3 + 44524/x^4 - 617624/x^5 + ... ) leads to the sequence given above. See A163931 and A163932 for more information. - Johannes W. Meijer, Oct 20 2009

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 = 0..100

FORMULA

a(n)=sum((-1)^(n+k)*binomial(k+2, 2)*5^k*stirling1(n+2, k+2), k=0..n). - Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004

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-2) = |f(n,2,5)|, for n>=2. [From Milan Janjic, Dec 21 2008]

MATHEMATICA

Table[Sum[(-1)^(n + k)*Binomial[k + 2, 2]*5^k*StirlingS1[n + 2, k + 2], {k, 0, n}], {n, 0, 20}] (* T. D. Noe, Aug 10 2012 *)

CROSSREFS

Sequence in context: A154241 A154250 A154350 * A060788 A144708 A020528

Adjacent sequences:  A001719 A001720 A001721 * A001723 A001724 A001725

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

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

STATUS

approved

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Last modified January 19 20:33 EST 2019. Contains 319310 sequences. (Running on oeis4.)