A096945 Eighth column of (1,5)-Pascal triangle A096940.

5, 36, 148, 456, 1170, 2640, 5412, 10296, 18447, 31460, 51480, 81328, 124644, 186048, 271320, 387600, 543609, 749892, 1019084, 1366200, 1808950, 2368080, 3067740, 3935880, 5004675, 6310980, 7896816, 9809888, 12104136, 14840320, 18086640, 21919392, 26423661, 31694052

Offset

0,1

Comments

If Y is a 5-subset of an n-set X then, for n >= 11, a(n-11) is the number of 7-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..33.

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

Formula

G.f.: (5-4*x)/(1-x)^8.

a(n) = (n+35)*binomial(n+6, 6)/7 = 5*b(n)-4*b(n-1), with b(n) = A000580(n+7) = binomial(n+7, 7).

a(n) = 8*a(n-1)-28*a(n-2)+56*a(n-3)-70*a(n-4)+56*a(n-5)- 28*a(n-6)+ 8*a(n-7)-a(n-8), with a(0)=5, a(1)=36, a(2)=148, a(3)=456, a(4)=1170, a(5)=2640, a(6)=5412, a(7)=10296. - Harvey P. Dale, Aug 16 2014

From Amiram Eldar, Oct 20 2025: (Start)

Sum_{n>=0} 1/a(n) = 601260273100596371/2522193712997587200.

Sum_{n>=0} (-1)^n/a(n) = 422464*log(2)/9889 - 816628475873935947089/27744130842973459200. (End)

Mathematica

CoefficientList[Series[(5-4*x)/(1-x)^8, {x, 0, 30}], x] (* Harvey P. Dale, Aug 16 2014 *)
(* Alternative: *)
LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {5, 36, 148, 456, 1170, 2640, 5412, 10296}, 30] (* Harvey P. Dale, Aug 16 2014 *)

Crossrefs

Cf. A096944 (seventh column), A096946 (ninth column).

Cf. A096940.

Sequence in context: A276249 A027765 A196481 * A063417 A109726 A272561

Adjacent sequences: A096942 A096943 A096944 * A096946 A096947 A096948

Keyword

nonn,easy,changed

Author

Wolfdieter Lang, Jul 16 2004

Status

approved