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A062990 Eighth column (r=7) of FS(5) staircase array A062985. 2
5, 30, 110, 315, 771, 1688, 3396, 6390, 11385, 19382, 31746, 50297, 77415, 116160, 170408, 245004, 345933, 480510, 657590, 887799, 1183787, 1560504, 2035500, 2629250, 3365505, 4271670, 5379210, 6724085, 8347215 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

In the Frey-Sellers reference this sequence is called {(n+2) over 7}_{4}, n >= 0.

REFERENCES

D.D. Frey, J. A. Sellers, Generalizing Bailey's generalization of the Catalan numbers, The Fibonacci Quarterly, 39 (2001) 142-148.

LINKS

Harry J. Smith, Table of n, a(n) for n=0,...,1000

Index entries for linear recurrences with constant coefficients, signature (8, -28, 56, -70, 56, -28, 8, -1).

FORMULA

a(n)= A062985(n+2, 7)=(n+1)*(n+2)*(n+3)*(n^4+29*n^3+326*n^2+1744*n+4200)/7!.

G.f.: N(5;1, x)/(1-x)^8 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.

binomial(n+7,n)-binomial(n+2,n)). - Zerinvary Lajos, Jun 23 2006

MAPLE

[seq((binomial(n+7, n)-binomial(n+2, n)), n=1..29)]; - Zerinvary Lajos, Jun 23 2006

MATHEMATICA

Table[Binomial[n+7, n]-Binomial[n+2, n], {n, 30}] (* or *) LinearRecurrence[ {8, -28, 56, -70, 56, -28, 8, -1}, {5, 30, 110, 315, 771, 1688, 3396, 6390}, 30] (* Harvey P. Dale, Jun 09 2016 *)

PROG

(PARI) { for (n=0, 1000, m=n + 1; a=binomial(m + 7, m) - binomial(m + 2, m); write("b062990.txt", n, " ", a) ) } [From Harry J. Smith, Aug 15 2009]

CROSSREFS

Partial sums of A062989.

Sequence in context: A071252 A174002 A030506 * A018213 A047661 A000649

Adjacent sequences:  A062987 A062988 A062989 * A062991 A062992 A062993

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Jul 12 2001

EXTENSIONS

More terms from Zerinvary Lajos, Jun 23 2006

STATUS

approved

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Last modified February 24 07:50 EST 2018. Contains 299599 sequences. (Running on oeis4.)