A062990 Eighth column (r=7) of FS(5) staircase array A062985.

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

Offset

0,1

Comments

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

a(n) = 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) ) } \\ Harry J. Smith, Aug 15 2009

Crossrefs

Partial sums of A062989.

Sequence in context: A071252 A174002 A030506 * A018213 A359975 A047661

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