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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

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

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

Cf. A000217, A000578.

Sequence in context: A211866 A327848 A034273 * A161512 A162347 A161879

Adjacent sequences:  A193572 A193573 A193574 * A193576 A193577 A193578

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Sep 08 2011

STATUS

approved

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Last modified August 1 02:28 EDT 2021. Contains 346377 sequences. (Running on oeis4.)