|
|
A268329
|
|
Expansion of (1 - sqrt(1 - 4*x))^5/16.
|
|
0
|
|
|
2, 10, 40, 150, 550, 2002, 7280, 26520, 96900, 355300, 1307504, 4828850, 17895150, 66533250, 248124000, 927983760, 3479939100, 13082337900, 49295766000, 186156379500, 704415740028, 2670587146260, 10142836030240, 38586876202000, 147029304149000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
5,1
|
|
COMMENTS
|
a(n) is the number of North-East paths from (0,0) to (n,n) that cross the diagonal vertically exactly once and horizontally exactly twice, and bounce off the diagonal to the right once but not to the left. Details about this sequence can be found in Section 4.5 in Pan and Remmel's link. - Ran Pan, Feb 01 2016
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (1 - sqrt(1 - 4*x))^5/16.
a(n) = 10 * binomial(2n-6,n-5)/n.
D-finite with recurrence: n*(n-5)*a(n) -2*(n-3)*(2*n-7)*a(n-1)=0. - R. J. Mathar, Feb 17 2016
|
|
MATHEMATICA
|
Table[10 Binomial[2 n - 6, n - 5]/n, {n, 5, 29}] (* or *)
Table[SeriesCoefficient[(1 - Sqrt[1 - 4 x])^5/16, {x, 0, n}], {n, 5, 29}] (* Michael De Vlieger, Feb 17 2016 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|