A062988 a(n) = binomial(n+6,5) - 1.

5, 20, 55, 125, 251, 461, 791, 1286, 2001, 3002, 4367, 6187, 8567, 11627, 15503, 20348, 26333, 33648, 42503, 53129, 65779, 80729, 98279, 118754, 142505, 169910, 201375, 237335, 278255, 324631

Offset: 0

Author

Wolfdieter Lang, Jul 12 2001

Keywords

• nonn
• easy

Comments

In the Frey-Sellers reference this sequence is called {(n+2) over 5}_{4}, n >= 0.

Links

• Harry J. Smith, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Sixth column (r=5) of FS(5) staircase array A062985.

A column of triangle A014473.

Cf. A000096, A062748, A063258.

Programs

Magma

[Binomial(n+6,5) -1: n in [0..40]]; // G. C. Greubel, Apr 25 2024

Maple

[seq(binomial(n+6,5)-1, n=0..35)]; # Zerinvary Lajos, Nov 25 2006

Mathematica

Binomial[Range[6,45],5] -1 (* G. C. Greubel, Apr 25 2024 *)

PARI

{ for (n=0, 1000, write("b062988.txt", n, " ", binomial(n + 6, 5) - 1) ) } \\ Harry J. Smith, Aug 15 2009

SageMath

[binomial(n+6,5) -1 for n in range(41)] # G. C. Greubel, Apr 25 2024

Formula

a(n) = A062985(n+2, 5).

a(n) = (n+1)*(n^4 + 19*n^3 + 136*n^2 + 444*n + 600)/5!.

G.f.: N(5;1, x)/(1-x)^6 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.

E.g.f.: (1/120)*(600 + 1800*x + 1200*x^2 + 300*x^3 + 30*x^4 + x^5)*exp(x). - G. C. Greubel, Apr 25 2024