A053310 a(n) = (n+3)*binomial(n+8, 8)/3.

1, 12, 75, 330, 1155, 3432, 9009, 21450, 47190, 97240, 189618, 352716, 629850, 1085280, 1812030, 2941884, 4657983, 7210500, 10935925, 16280550, 23828805, 34337160, 48774375, 68368950, 94664700, 129585456, 175509972, 235358200

Offset: 0

Author

Barry E. Williams, Mar 06 2000

Keywords

• easy
• nonn

Comments

If Y is a 3-subset of an n-set X then, for n>=11, a(n-11) is the number of 11-subsets of X having at least two elements in common with Y. - Milan Janjic, Nov 23 2007

References

• A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189, 194-196.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

Partial sums of A053367.

Cf. A053367, A053347, A000581.

Cf. A093560 ((3, 1) Pascal, column m=9).

Programs

Magma

[(n+3)*Binomial(n+8, 8)/3: n in [0..30]]; // G. C. Greubel, May 24 2018

Mathematica

CoefficientList[Series[(1+2*x)/(1-x)^10, {x, 0, 50}], x] (* G. C. Greubel, May 24 2018 *)
Table[(n+3) Binomial[n+8,8]/3,{n,0,30}] (* or *) LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{1,12,75,330,1155,3432,9009,21450,47190,97240},30] (* Harvey P. Dale, Feb 25 2021 *)

PARI

for(n=0, 30, print1((n+3)*binomial(n+8, 8)/3, ", ")) \\ G. C. Greubel, May 24 2018

Formula

G.f.: (1+2*x)/(1-x)^10.

a(n) = binomial(n+8,n+2)*binomial(n+3,n)/28. - Zerinvary Lajos, May 12 2006