A096943 Sixth column of (1,5)-Pascal triangle A096940.

5, 26, 81, 196, 406, 756, 1302, 2112, 3267, 4862, 7007, 9828, 13468, 18088, 23868, 31008, 39729, 50274, 62909, 77924, 95634, 116380, 140530, 168480, 200655, 237510, 279531, 327236, 381176, 441936, 510136, 586432, 671517, 766122, 871017, 987012, 1114958, 1255748

Offset

0,1

Comments

If Y is a 5-subset of an n-set X then, for n >= 9, a(n-9) is the number of 5-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..37.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

G.f.: (5-4*x)/(1-x)^6.

a(n) = (n+25)*binomial(n+4, 4)/5 = 5*b(n)-4*b(n-1), with b(n) = A000389(n+5) = binomial(n+5, 5).

a(n) = 6*a(n-1)- 15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6), with a(0)=5, a(1)=26, a(2)=81, a(3)=196, a(4)=406, a(5)=756. - Harvey P. Dale, Jan 11 2014

From Amiram Eldar, Oct 19 2025: (Start)

Sum_{n>=0} 1/a(n) = 331302257155/1264311912864.

Sum_{n>=0} (-1)^n/a(n) = 3440*log(2)/483 - 54234801626651/11378807215776. (End)

Mathematica

CoefficientList[Series[(5-4x)/(1-x)^6, {x, 0, 40}], x] (* or *) LinearRecurrence[ {6, -15, 20, -15, 6, -1}, {5, 26, 81, 196, 406, 756}, 40] (* Harvey P. Dale, Jan 11 2014 *)

Crossrefs

Cf. A096942 (fifth column), A096944 (seventh column).

Cf. A000389, A096940.

Sequence in context: A254831 A360350 A145013 * A166810 A210367 A261347

Adjacent sequences: A096940 A096941 A096942 * A096944 A096945 A096946

Keyword

nonn,easy

Author

Wolfdieter Lang, Jul 16 2004

Status

approved