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a(n) = round((n-1)^2*(n+5)/144).
2

%I #14 Sep 08 2022 08:45:02

%S 0,0,0,0,1,1,2,3,4,6,8,11,14,18,22,27,33,39,46,54,63,72,83,94,107,120,

%T 135,150,167,185,204,225,247,270,295,321,349,378,409,441,475,511,549,

%U 588,629,672,717,764,813,864,917,972,1030,1089,1151,1215

%N a(n) = round((n-1)^2*(n+5)/144).

%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 120, see P(n,4).

%H Harry J. Smith, <a href="/A059291/b059291.txt">Table of n, a(n) for n = 0..1000</a>

%t Table[Round[(n-1)^2*(n+5)/144], {n, 0, 50}] (* _G. C. Greubel_, Jan 04 2017 *)

%o (PARI) { default(realprecision, 100); for (n = 0, 1000, write("b059291.txt", n, " ", round((n - 1)^2*(n + 5)/144)); ) } \\ _Harry J. Smith_, Jun 25 2009

%o (Magma) [Round((n-1)^2*(n+5)/144): n in [0..80]]; // _Vincenzo Librandi_, Jan 05 2017

%Y Cf. A001400, A059290.

%K nonn

%O 0,7

%A _N. J. A. Sloane_, Jan 25 2001