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 A001706 Generalized Stirling numbers. (Formerly M4646 N1988) 7
 1, 9, 71, 580, 5104, 48860, 509004, 5753736, 70290936, 924118272, 13020978816, 195869441664, 3134328981120, 53180752331520, 953884282141440, 18037635241029120, 358689683932346880, 7483713725055744000, 163478034254755584000, 3731670622213083648000 (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=2) ~ exp(-x)/x^3*(1 - 9/x + 71/x^2 - 580/x^3 + 5104/x^4 - 48860/x^5+ the sequence given above. See A163931 and A163932 for more information. - Johannes W. Meijer, Oct 20 2009 a(n-1) is equal to -1 times the coefficient of x of the characteristic polynomial of the n X n matrix whose (i,j)-entry is equal to i+3 if i=j and is equal to 1 otherwise. - John M. Campbell, May 24 2011 REFERENCES 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 D. S. Mitrinovic, R. S. Mitrinovic, Tableaux d'une classe de nombres reliĆ©s aux nombres de Stirling, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 77 1962, 77 pp. 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] FORMULA E.g.f. (with offset 2): log(1 - x)^2 / (2 * (1 - x)^2). a(n) = Sum_{k=0..n}(-1)^(n+k)*binomial(k+2, 2)*2^k*stirling1(n+2, k+2). - Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004 a(n-1) = (1/2)*Sum_{i=0..n} binomial(n, i)*A000254(i)*A000254(n-i). - Benoit Cloitre, Mar 09 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-1) = |f(n,2,2)|, for n>=2. - Milan Janjic, Dec 21 2008 a(n) = (n+3)!*((gamma-1)*Psi(n+4)+2+gamma^2-17*gamma/6+sum(Psi(i+4)/(i+4),i = 0 .. n-1)). - Mark van Hoeij, Oct 26 2011 MATHEMATICA Table[-Coefficient[CharacteristicPolynomial[Array[KroneckerDelta[#1, #2]((((#1+3)))-1)+1&, {n, n}], x], x, 1], {n, 1, 10}] (* John M. Campbell, May 24 2011 *) CROSSREFS Sequence in context: A178869 A057080 A287819 * A251284 A324413 A144745 Adjacent sequences:  A001703 A001704 A001705 * A001707 A001708 A001709 KEYWORD nonn AUTHOR EXTENSIONS More terms from Christian G. Bower STATUS approved

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Last modified October 19 14:36 EDT 2019. Contains 328222 sequences. (Running on oeis4.)