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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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified December 6 04:14 EST 2019. Contains 329784 sequences. (Running on oeis4.)