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, 245444980, 317443720, 407529100

Offset

0,1

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

Table of n, a(n) for n=0..30.

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

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.

From Amiram Eldar, Oct 20 2025: (Start)

Sum_{n>=0} 1/a(n) = 42247826259879289968150251/185495372738071817125504800.

Sum_{n>=0} (-1)^n/a(n) = 193174272*log(2)/848003 - 29255701892781921744165279979/185495372738071817125504800. (End)

Mathematica

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

Crossrefs

Cf. A000582, A096940, A096946 (ninth column).

Sequence in context: A348786 A318550 A318212 * A042533 A355056 A309185

Adjacent sequences: A096944 A096945 A096946 * A096948 A096949 A096950

Keyword

nonn,easy

Author

Wolfdieter Lang, Jul 16 2004

Status

approved