OFFSET
0,2
COMMENTS
In the Frey-Sellers reference this sequence is called {(n+2) over 6}_{4}, n >= 0.
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..1000
D. D. Frey and J. A. Sellers, Generalizing Bailey's generalization of the Catalan numbers, The Fibonacci Quarterly, 39 (2001) 142-148.
Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).
FORMULA
a(n) = A062985(n+2, 6) = (n+1)*(n+2)*(n^4 + 24*n^3 + 221*n^2 + 954*n + 1800)/6!.
G.f.: N(5;1, x)/(1-x)^7 with N(5;1, x)= 5-10*x+10*x^2-5*x^3+x^4 = (1-(1-x)^5)/x polynomial of second row of A062986.
a(0)=0, a(1)=5, a(2)=25, a(3)=80, a(4)=205, a(5)=456, a(6)=917, a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7). - Harvey P. Dale, Aug 08 2013
D-finite with recurrence -n*a(n) +(n+6)*a(n-1) +5*n=0. - R. J. Mathar, Nov 22 2024
MATHEMATICA
Table[Binomial[n+6, 6]-n-1, {n, 0, 40}] (* OR *) LinearRecurrence[ {7, -21, 35, -35, 21, -7, 1}, {0, 5, 25, 80, 205, 456, 917}, 40] (* Harvey P. Dale, Aug 08 2013 *)
PROG
(PARI) { for (n=0, 1000, write("b062989.txt", n, " ", binomial(n + 6, 6) - n - 1) ) } \\ Harry J. Smith, Aug 15 2009
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Wolfdieter Lang, Jul 12 2001
EXTENSIONS
Simpler definition from Zerinvary Lajos, May 08 2006
STATUS
approved