

A062749


Sixth column (r=5) of FS(3) staircase array A062745.


2



12, 43, 108, 228, 431, 753, 1239, 1944, 2934, 4287, 6094, 8460, 11505, 15365, 20193, 26160, 33456, 42291, 52896, 65524, 80451, 97977, 118427, 142152, 169530, 200967, 236898, 277788, 324133, 376461
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OFFSET

0,1


COMMENTS

In the FreySellers 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) 142148.
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)/(1x)^6 with N(3;2, x)= 1229*x+30*x^215*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(n1)  15*a(n2) + 20*a(n3)  15*a(n4) + 6*a(n5)  a(n6) for n>5.
(End)


MAPLE

seq(coeff(series((3*x^415*x^3+30*x^229*x+12)/(1x)^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

Sequence in context: A082829 A003357 A004466 * A251929 A004636 A136279
Adjacent sequences: A062746 A062747 A062748 * A062750 A062751 A062752


KEYWORD

nonn,easy


AUTHOR

Wolfdieter Lang, Jul 12 2001


STATUS

approved



