OFFSET
0,1
COMMENTS
In the Frey-Sellers reference this sequence is called {(n+2) over 6}_{3}, 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) = A062750(n+2, 6) = (n+10)*(n+3)*(n+2)*(n+1)*(n^2+11*n+48)/6!.
G.f.: = (x-2)*(x^2-2*x+2)/(x-1)^7 = N(4;1, x)/(1-x)^7 with N(4;1, x) = 4-6*x+4*x^2-x^3, polynomial of second row of A062751.
a(0)=4, a(1)=22, a(2)=74, a(3)=195, a(4)=441, a(5)=896, a(6)=1680, 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, May 02 2012
MATHEMATICA
Table[Sum[Binomial[i+n, n], {i, 3, 6}], {n, 0, 30}] (* or *) LinearRecurrence[ {7, -21, 35, -35, 21, -7, 1}, {4, 22, 74, 195, 441, 896, 1680}, 30] (* Harvey P. Dale, May 02 2012 *)
PROG
(PARI) { for (n=0, 1000, a=binomial(3 + n, n) + binomial(4 + n, n) + binomial(5 + n, n) + binomial(6 + n, n); write("b062966.txt", n, " ", a) ) } \\ Harry J. Smith, Aug 14 2009
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Wolfdieter Lang, Jul 12 2001
EXTENSIONS
Better description from Zerinvary Lajos, Dec 02 2005
STATUS
approved