A096947 Tenth column of (1,5)-Pascal triangle A096940.

5, 46, 235, 880, 2695, 7150, 17017, 37180, 75790, 145860, 267410, 470288, 797810, 1311380, 2096270, 3268760, 4984859, 7450850, 10935925, 15787200, 22447425, 31475730, 43571775, 59603700, 80640300, 107987880, 143232276, 188286560

Offset: 0

Author

Wolfdieter Lang, Jul 16 2004

Keywords

• nonn
• easy

Comments

If Y is a 5-subset of an n-set X then, for n>=13, a(n-13) is the number of 9-subsets of X having at most one element in common with Y. - Milan Janjic, Dec 08 2007

Links

• Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

Ninth column: A096946.

Programs

Mathematica

CoefficientList[Series[(5-4x)/(1-x)^10,{x,0,40}],x] (* Harvey P. Dale, Jan 06 2020 *)

Formula

a(n) = (n+45)*binomial(n+8, 8)/9.

a(n) = 5*b(n)-4*b(n-1), with b(n) = A000582(n+9) = binomial(n+9, 9).

G.f.: (5-4*x)/(1-x)^10.