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A193575 T(n)^3 - n^3 where T(n) is a triangular number. 1
0, 19, 189, 936, 3250, 9045, 21609, 46144, 90396, 165375, 286165, 472824, 751374, 1154881, 1724625, 2511360, 3576664, 4994379, 6852141, 9253000, 12317130, 16183629, 21012409, 26986176, 34312500, 43225975, 53990469, 66901464, 82288486, 100517625, 121994145 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
a(n) = (n^3*(n^3+3*n^2+3*n-7)/8) = (1/8)*(n-1)*(n^2+4*n+7)*n^3.
From Wesley Ivan Hurt, Aug 23 2014: (Start)
G.f.: x^2*(19+56*x+12*x^2+2*x^3+x^4)/(1-x)^7.
a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7).
a(n) = sum_{i=1..n} sum_{j=1..n} sum_{k=1..n} (i*j*k-1).
a(n) = A000217(n)^3 - A000578(n), n > 0.
(End)
MAPLE
A193575:=n->n^3*(n^3+3*n^2+3*n-7)/8: seq(A193575(n), n=1..40); # Wesley Ivan Hurt, Aug 23 2014
MATHEMATICA
Table[n^3*(n^3 + 3*n^2 + 3*n - 7)/8, {n, 40}] (* Wesley Ivan Hurt, Aug 23 2014 *)
CoefficientList[Series[x*(19 + 56 x + 12 x^2 + 2 x^3 + x^4)/(1 - x)^7, {x, 0, 30}], x] (* Wesley Ivan Hurt, Aug 23 2014 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 19, 189, 936, 3250, 9045, 21609}, 40] (* Harvey P. Dale, Oct 24 2020 *)
PROG
(Magma) [(n^3*(n^3+3*n^2+3*n-7)/8): n in [1..40]]
CROSSREFS
Sequence in context: A211866 A327848 A034273 * A161512 A162347 A161879
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Sep 08 2011
STATUS
approved

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Last modified April 22 01:34 EDT 2024. Contains 371887 sequences. (Running on oeis4.)