A096944 Seventh column of (1,5)-Pascal triangle A096940.

5, 31, 112, 308, 714, 1470, 2772, 4884, 8151, 13013, 20020, 29848, 43316, 61404, 85272, 116280, 156009, 206283, 269192, 347116, 442750, 559130, 699660, 868140, 1068795, 1306305, 1585836, 1913072, 2294248, 2736184, 3246320, 3832752, 4504269, 5270391, 6141408, 7128420

Offset

0,1

Comments

If Y is a 5-subset of an n-set X then, for n >= 10, a(n-10) is the number of 6-subsets of X having at most one element in common with Y. > - Milan Janjic, Dec 08 2007

Links

Table of n, a(n) for n=0..35.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

G.f.: (5-4*x)/(1-x)^7.

a(n) = (n+30)*binomial(n+5, 5)/6 = 5*b(n)-4*b(n-1), with b(n) = A000579(n+6) = binomial(n+6, 6).

From Amiram Eldar, Oct 20 2025: (Start)

Sum_{n>=0} 1/a(n) = 11407209094463887/46098505171719000.

Sum_{n>=0} (-1)^n/a(n) = 7744*log(2)/435 - 80114179503603871/6585500738817000. (End)

Mathematica

a[n_] := (n+30) * Binomial[n+5, 5]/6; Array[a, 30, 0] (* Amiram Eldar, Oct 20 2025 *)

Crossrefs

Cf. A096943 (sixth column), A096945 (eighth column).

Cf. A000579, A096940.

Sequence in context: A183520 A099083 A212523 * A053699 A152122 A260045

Adjacent sequences: A096941 A096942 A096943 * A096945 A096946 A096947

Keyword

nonn,easy

Author

Wolfdieter Lang, Jul 16 2004

Status

approved