cp's OEIS Frontend

A001722 Generalized Stirling numbers.

%I A001722 M5061 N2191 #22 Dec 24 2021 08:17:35
%S A001722 1,18,251,3325,44524,617624,8969148,136954044,2201931576,37272482280,
%T A001722 663644774880,12413008539360,243533741849280,5003753991174720,
%U A001722 107497490419296000,2410964056571616000,56366432074677312000,1371711629236971456000,34699437370290760704000
%N A001722 Generalized Stirling numbers.
%C A001722 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
%D A001722 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001722 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001722 T. D. Noe, <a href="/A001722/b001722.txt">Table of n, a(n) for n = 0..100</a>
%H A001722 D. S. Mitrinovic and R. S. Mitrinovic, <a href="http://pefmath2.etf.rs/files/47/77.pdf">Tableaux d'une classe de nombres reliés aux nombres de Stirling</a>, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 77 1962, 77 pp.
%F A001722 a(n) = Sum_{k=0..n} (-1)^(n+k)*binomial(k+2, 2)*5^k*Stirling1(n+2, k+2). - Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004
%F A001722 If we define f(n,i,a) = Sum_{k=0..n-i} binomial(n,k)*Stirling1(n-k,i)*Product_{j=0..k-1} (-a-j), then a(n-2) = |f(n,2,5)|, for n >= 2. - _Milan Janjic_, Dec 21 2008
%t A001722 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 *)
%K A001722 nonn
%O A001722 0,2
%A A001722 _N. J. A. Sloane_
%E A001722 More terms from Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004