A095819 Tenth column (m=9) of (1,4)-Pascal triangle A095666.

4, 37, 190, 715, 2200, 5863, 14014, 30745, 62920, 121550, 223652, 394706, 671840, 1107890, 1776500, 2778446, 4249388, 6369275, 9373650, 13567125, 19339320, 27183585, 37718850, 51714975, 70122000, 94103724, 125076072, 164750740, 215184640, 278835700, 358625608

Offset

0,1

Comments

If Y is a 4-subset of an n-set X then, for n >= 12, a(n-12) 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

G.f.: (4-3*x)/(1-x)^10.

a(n) = 4*b(n)-3*b(n-1) = (n+36)*binomial(n+8, 8)/9, with b(n) = binomial(n+9, 9) = A000582(n+9, 9).

From Amiram Eldar, Oct 21 2025: (Start)

Sum_{n>=0} 1/a(n) = 9765230763658496531/34329858871356048000.

Sum_{n>=0} (-1)^n/a(n) = 101442816*log(2)/346115 - 76631112772286475409711/377628447584916528000. (End)

Mathematica

a[n_] := (n+36) * Binomial[n+8, 8] / 9; Array[a, 30, 0] (* Amiram Eldar, Oct 21 2025 *)

Crossrefs

Cf. A000582, A095666.

Sequence in context: A297745 A273684 A063418 * A335773 A201865 A025542

Adjacent sequences: A095816 A095817 A095818 * A095820 A095821 A095822

Keyword

nonn,easy

Author

Wolfdieter Lang, Jun 11 2004

Status

approved