|
| |
|
|
A000457
|
|
Exponential generating function: (1+3*x)/(1-2*x)^(7/2).
(Formerly M4736 N2028)
|
|
17
|
|
|
|
1, 10, 105, 1260, 17325, 270270, 4729725, 91891800, 1964187225, 45831035250, 1159525191825, 31623414322500, 924984868933125, 28887988983603750, 959493919812553125, 33774185977401870000, 1255977541034632040625
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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. Budapest, 1939, p. 152.
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
|
|
|
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
|
Equals (1/2)*A000906.
Third column of triangle A001497.
Second column (m=1) of unsigned Laguerre-Sonin a=1/2 triangle |A130757|.
Cf. A160473, A163939.
Sequence in context: A123512 A079515 A024131 * A240681 A113348 A193274
Adjacent sequences: A000454 A000455 A000456 * A000458 A000459 A000460
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
N. J. A. Sloane
|
|
|
EXTENSIONS
|
More terms from Sascha Kurz, Aug 15 2002
|
|
|
STATUS
|
approved
|
| |
|
|
