A095664 Ninth column (m=8) of (1,3)-Pascal triangle A095660.

3, 25, 117, 405, 1155, 2871, 6435, 13299, 25740, 47190, 82654, 139230, 226746, 358530, 552330, 831402, 1225785, 1773783, 2523675, 3535675, 4884165, 6660225, 8974485, 11960325, 15777450, 20615868, 26700300, 34295052, 43709380, 55303380, 69494436, 86764260, 107666559, 132835365, 162994065

Offset

0,1

Comments

If Y is a 3-subset of an n-set X then, for n >= 10, a(n-10) is the number of 8-subsets of X having at most one element in common with Y. - Milan Janjic, Nov 23 2007

Links

Table of n, a(n) for n=0..34.

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

a(n) = binomial(n+7, 7)*(n+24)/8 = 3*b(n)-2*b(n-1), with b(n) = binomial(n+8, 8); cf. A000581.

G.f.: (3-2*x)/(1-x)^9.

From Amiram Eldar, Oct 21 2025: (Start)

Sum_{n>=0} 1/a(n) = 21105211872137/54692778730590.

Sum_{n>=0} (-1)^n/a(n) = 1336320*log(2)/7429 - 20408471306318741/164078336191770. (End)

Mathematica

a[n_] := Binomial[n+7, 7] * (n+24)/8; Array[a, 30, 0] (* Amiram Eldar, Oct 21 2025 *)

Prog

(PARI) my(x='x+O('x^66)); Vec((3-2*x)/(1-x)^9) \\ Joerg Arndt, May 11 2013

Crossrefs

Cf. A095663 (eighth column), A095665 (tenth column).

Cf. A000581, A095660.

Sequence in context: A201534 A059457 A165206 * A215773 A377555 A099868

Adjacent sequences: A095661 A095662 A095663 * A095665 A095666 A095667

Keyword

nonn,easy

Author

Wolfdieter Lang, Jun 11 2004

Status

approved