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 A000504 S2(j,2j+3) where S2(n,k) is a 2-associated Stirling number of the second kind. (Formerly M5315 N2309) 2
 1, 56, 1918, 56980, 1636635, 47507460, 1422280860, 44346982680, 1446733012725, 49473074851200, 1774073543492250, 66681131440423500, 2624634287988087375, 108060337458000427500, 4647703259223579555000, 208548093035794902390000, 9749651260035434678555625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 256. 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). F. N. David and D. E. Barton, Combinatorial Chance. Hafner, NY, 1962, p. 296. LINKS H. W. Gould, Harris Kwong, Jocelyn Quaintance, On Certain Sums of Stirling Numbers with Binomial Coefficients, J. Integer Sequences, 18 (2015), #15.9.6. M. Ward, The representations of Stirling's numbers and Stirling's polynomials as sums of factorials, Amer. J. Math., 56 (1934), p. 87-95. FORMULA It appears a(n) = 2^(n+1)*GAMMA(n+5/2)*(n^2+n)*(10*n^2+15*n+2)/(405*Pi^(1/2)). - Mark van Hoeij,  Oct 26 2011. G.f.: x*(7*(5-30*x) * hypergeom([4, 9/2],[],2*x) - 26*hypergeom([3, 7/2],[],2*x))/9. - Mark van Hoeij,  Apr 07 2013 (n-1)*(10*n^2-5*n-3)*a(n) - (2*n+3)*(n+1)*(10*n^2+15*n+2)*a(n-1) = 0. - R. J. Mathar, Jun 09 2018 MAPLE gf := (u, t)->exp(u*(exp(t)-1-t)); S2a := j->simplify(subs(u=0, t=0, diff(gf(u, t), u\$j, t\$(2*j+3)))/j!); for i from 1 to 20 do S2a(i); od; # Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Dec 12 2000 MATHEMATICA a[n_] := n (n+1) (10n^2+15n+2) (2n+3)!! / 810; Array[a, 20] (* Jean-François Alcover, Feb 09 2016, after Mark van Hoeij *) CROSSREFS Cf. A008299, A000497. Sequence in context: A140406 A075512 A223958 * A130646 A038649 A004375 Adjacent sequences:  A000501 A000502 A000503 * A000505 A000506 A000507 KEYWORD nonn AUTHOR EXTENSIONS More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Dec 12 2000 STATUS approved

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Last modified October 16 13:29 EDT 2019. Contains 328091 sequences. (Running on oeis4.)