OFFSET
0,2
REFERENCES
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 256.
F. N. David and D. E. Barton, Combinatorial Chance. Hafner, NY, 1962, p. 296.
C. Jordan, Calculus of Finite Differences. Eggenberger, Budapest and R�ttig-Romwalter, Sopron 1939; Chelsea, NY, 1965, p. 172.
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
G. C. Greubel, Table of n, a(n) for n = 0..200
Selden Crary, Richard Diehl Martinez, and Michael Saunders, The Nu Class of Low-Degree-Truncated Rational Multifunctions. Ib. Integrals of Matern-correlation functions for all odd-half-integer class parameters, arXiv:1707.00705 [stat.ME], 2017, Table 1.
H. W. Gould, Harris Kwong, and Jocelyn Quaintance, On Certain Sums of Stirling Numbers with Binomial Coefficients, J. Integer Sequences, 18 (2015), #15.9.6.
C. Jordan, On Stirling's Numbers, Tohoku Math. J., 37 (1933), 254-278.
Alexander Kreinin, Integer Sequences Connected to the Laplace Continued Fraction and Ramanujan's Identity, Journal of Integer Sequences, 19 (2016), #16.6.2.
J. Riordan, Notes to N. J. A. Sloane, Jul. 1968
Eric Weisstein's World of Mathematics, Stirling Number of the First Kind.
FORMULA
a(n) = (2n+3)!/( 3!*n!*2^n ).
a(n) = (n+1)*(2*n+3)!!/3, n>=0, with (2*n+3)!! = A001147(n+2).
a(n) = Sum_{j=0..n} (j + 1) * Eulerian2(n + 2, n - j). - Peter Luschny, Feb 13 2023
EXAMPLE
G.f. = 1 + 10*x + 105*x^2 + 1260*x^3 + 17325*x^4 + 270270*x^5 + ... - Michael Somos, Dec 15 2023
MATHEMATICA
Table[(2n+3)!/(3!*n!*2^n), {n, 0, 30}] (* G. C. Greubel, May 15 2018 *)
PROG
(PARI) for(n=0, 30, print1((2*n+3)!/(3!*n!*2^n), ", ")) \\ G. C. Greubel, May 15 2018
(Magma) [Factorial(2*n+3)/(6*Factorial(n)*2^n): n in [0..30]]; // G. C. Greubel, May 15 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Sascha Kurz, Aug 15 2002
STATUS
approved