OFFSET
0,1
COMMENTS
In the Frey-Sellers reference this sequence is called {(n+3) over 5}_{2}, n >= 0.
LINKS
Colin Barker, 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 (6,-15,20,-15,6,-1).
FORMULA
a(n) = A062745(n+3, 5)= -3+binomial(n+4, 3)*(n^2+16*n+75)/20 = (n+1)*(n^4+24*n^3+221*n^2+894*n+1440)/5!.
G.f.: N(3;2, x)/(1-x)^6 with N(3;2, x)= 12-29*x+30*x^2-15*x^3+3*x^4, polynomial of the third row of A062746.
From Colin Barker, Oct 30 2018: (Start)
G.f.: (12 - 29*x + 30*x^2 - 15*x^3 + 3*x^4) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>5.
(End)
MAPLE
seq(coeff(series((3*x^4-15*x^3+30*x^2-29*x+12)/(1-x)^6, x, n+1), x, n), n = 0 .. 30); # Muniru A Asiru, Oct 30 2018
PROG
(PARI) Vec((12 - 29*x + 30*x^2 - 15*x^3 + 3*x^4) / (1 - x)^6 + O(x^40)) \\ Colin Barker, Oct 30 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jul 12 2001
STATUS
approved