OFFSET
0,4
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
a(n) = C(n,2) + 42*C(n,3) + 375*C(n,4) + 1450*C(n,5) + 2940*C(n,6) + 3360*C(n,7) + 1680*C(n,8).
a(n) = (1/24)*(n^8 - 12*n^7 + 84*n^6 - 340*n^5 + 814*n^4 - 1130*n^3 + 829*n^2 - 246*n).
EXAMPLE
a(2) = binomial(2,2) = 1. The only transitive relation with four ordered pairs on the 2-set {1,2} is {(1,1),(1,2),(2,1),(2,2)}.
MATHEMATICA
A349849[n_] := Total[{1, 42, 375, 1450, 2940, 3360, 1680}*Binomial[n, Range[2, 8]]];
Array[A349849, 30, 0] (* or *)
LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {0, 0, 1, 45, 549, 3755, 18120, 69006, 220710}, 30] (* Paolo Xausa, Mar 24 2026 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Firdous Ahmad Mala, Dec 06 2021
STATUS
approved