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n*(n+5)*(50+45*n+n^2)/24.
2

%I #9 Jun 17 2017 03:06:05

%S 24,84,194,369,625,979,1449,2054,2814,3750,4884,6239,7839,9709,11875,

%T 14364,17204,20424,24054,28125,32669,37719,43309,49474,56250,63674,

%U 71784,80619,90219,100625,111879,124024,137104,151164,166250,182409

%N n*(n+5)*(50+45*n+n^2)/24.

%C Essentially the partial sums of A101860.

%C 5th partial summation within series as series accumulate n times from an initial sequence of Euler Triangle's row 4: 1,11,11,1: 5th row of the array in the examples of A101860.

%H C. Rossiter, <a href="http://noticingnumbers.net/300SeriesCube.htm">Depictions, Explorations and Formulas of the Euler/Pascal Cube</a>.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F G.f. x*(x-2)*(x^2-12*x+12) / (x-1)^5 . - R. J. Mathar, Dec 06 2011

%K easy,nonn

%O 1,1

%A Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 18 2004