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

Author

Wolfdieter Lang, Jul 12 2001

Keywords

• nonn
• easy

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).

Crossrefs

Partial sums of A062989.

Programs

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 *)

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

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

Extensions

More terms from Zerinvary Lajos, Jun 23 2006