A096942 Fifth column of (1,5)-Pascal triangle A096940.

5, 21, 55, 115, 210, 350, 546, 810, 1155, 1595, 2145, 2821, 3640, 4620, 5780, 7140, 8721, 10545, 12635, 15015, 17710, 20746, 24150, 27950, 32175, 36855, 42021, 47705, 53940, 60760, 68200, 76296, 85085, 94605, 104895, 115995, 127946, 140790, 154570, 169330, 185115

Offset

0,1

Comments

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = (n+20)*binomial(n+3, 3)/4 = 5*b(n) - 4*b(n-1), with b(n) = A000332(n+4) = binomial(n+4, 4).

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

a(n) = Sum_{k=1..n} (Sum_{i=1..k} i*(n-k+5)). - Wesley Ivan Hurt, Sep 26 2013

From Amiram Eldar, Oct 19 2025: (Start)

Sum_{n>=0} 1/a(n) = 5435530879/18797999220.

Sum_{n>=0} (-1)^n/a(n) = 864*log(2)/323 - 19052617079/11278799532. (End)

Mathematica

Table[(n + 20) Binomial[n + 3, 3]/4, {n, 0, 100}]
CoefficientList[Series[(5 - 4 x)/(1 - x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Oct 01 2013 *)

Prog

(Magma) [(n + 20)*Binomial(n + 3, 3) div 4: n in [0..50]]; // Vincenzo Librandi, Oct 01 2013

Crossrefs

Cf. A096941 (fourth column), A096943 (sixth column).

Cf. A000332, A096940.

Sequence in context: A147834 A160378 A201440 * A365300 A122244 A146854

Adjacent sequences: A096939 A096940 A096941 * A096943 A096944 A096945

Keyword

nonn,easy

Author

Wolfdieter Lang, Jul 16 2004

Status

approved