A095668 Sixth column (m=5) of (1,4)-Pascal triangle A095666.

4, 21, 66, 161, 336, 630, 1092, 1782, 2772, 4147, 6006, 8463, 11648, 15708, 20808, 27132, 34884, 44289, 55594, 69069, 85008, 103730, 125580, 150930, 180180, 213759, 252126, 295771, 345216, 401016, 463760, 534072, 612612, 700077, 797202, 904761

Offset

0,1

Comments

If Y is a 4-subset of an n-set X, then, for n >= 8, a(n-8) is the number of 5-subsets of X having at most one element in common with Y. - Milan Janjic, Dec 08 2007

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

G.f.: (4-3*x)/(1-x)^6.

a(n) = (n+20)*binomial(n+4, 4)/5.

a(n) = 4*b(n) - 3*b(n-1), with b(n) = binomial(n+5, 5) = A000389(n+5, 5).

E.g.f.: (480 + 2040*x + 1680*x^2 + 440*x^3 + 40*x^4 + x^5)*exp(x)/120. - G. C. Greubel, Nov 25 2017

a(n) = Sum_{i=0..n+1} A000217(i)*A055999(n+2-i). - Bruno Berselli, Mar 05 2018

Maple

A095668:=n->(n+20)*binomial(n+4, 4)/5: seq(A095668(n), n=0..80); # Wesley Ivan Hurt, Nov 25 2017

Mathematica

Table[(n + 20)*Binomial[n + 4, 4]/5, {n, 0, 50}] (* G. C. Greubel, Nov 25 2017 *)

Prog

(PARI) for(n=0, 30, print1((n+20)*binomial(n+4, 4)/5, ", ")) \\ G. C. Greubel, Nov 25 2017
(Magma) [(n+20)*Binomial(n+4, 4)/5: n in [0..30]]; // G. C. Greubel, Nov 25 2017

Crossrefs

Cf. A000389, A095666.

Cf. A000217, A055999.

Sequence in context: A089893 A212246 A359065 * A078800 A184706 A034960

Adjacent sequences: A095665 A095666 A095667 * A095669 A095670 A095671

Keyword

nonn,easy

Author

Wolfdieter Lang, Jun 11 2004

Status

approved