OFFSET
0,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Matthew House, Table of n, a(n) for n = 0..10000
G. Kreweras, Sur une classe de problèmes de dénombrement liés au treillis des partitions des entiers, Cahiers du Bureau Universitaire de Recherche Opérationnelle, Institut de Statistique, Université de Paris, 6 (1965), circa p. 82.
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
a(n) = (n*(1 + n)^2*(2 + n)^2*(3 + n)*(1 + 2*n)*(3 + 2*n)*(5 + 2*n))/7560.
G.f.: 2*(1 + 20*x + 75*x^2 + 75*x^3 + 20*x^4 + x^5)/(1-x)^10.
MATHEMATICA
Abs@ With[{n = 4}, Table[(2 (-1)^(n + k) (n + k - 1)! (2 n + 2 k - 3)!)/(n! k! (2 n - 1)! (2 k - 1)!), {k, 0, 24}]] (* or *)
{0}~Join~CoefficientList[Series[2 (1 + 20 x + 75 x^2 + 75 x^3 + 20 x^4 + x^5)/(1 - x)^10, {x, 0, 23}], x] (* Michael De Vlieger, Mar 26 2016 *)
LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 2, 60, 660, 4290, 20020, 74256, 232560, 639540, 1586310}, 30] (* Harvey P. Dale, Jan 01 2017 *)
PROG
(PARI) a(n) = (n*(1 + n)^2*(2 + n)^2*(3 + n)*(1 + 2*n)*(3 + 2*n)*(5 + 2*n))/7560 \\ Charles R Greathouse IV, Jul 28 2015
(PARI) x='x+O('x^99); concat(0, Vec(2*(1+20*x+75*x^2+75*x^3+20*x^4+x^5)/(1-x)^10)) \\ Altug Alkan, Mar 26 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved