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
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Dec 12 2000
STATUS
approved