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 A099764 a(n) = n^2 * (n+1)^2 * (n+2)^2 = 36*A001249(n-1). 2
 0, 36, 576, 3600, 14400, 44100, 112896, 254016, 518400, 980100, 1742400, 2944656, 4769856, 7452900, 11289600, 16646400, 23970816, 33802596, 46785600, 63680400, 85377600, 112911876, 147476736, 190440000, 243360000, 308002500, 386358336 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES Jolley, Summation of Series, Dover (1961). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1). FORMULA sum_{n=1..infinity} 1/a(n) = Pi^2/4-39/16 =  0.029901100272... [Jolley eq 241] G.f.: -36*x*(1+x)*(x^2+8*x+1) / (x-1)^7 . - R. J. Mathar, Oct 03 2011 a(n) = (Sum_{k=0..n} (2*k+1))^3 - Sum_{k=0..n} (2*k+1)^3. - Philippe Deléham, Mar 10 2014 a(n) = A001014(n+1) - A002593(n+1). - Philippe Deléham, Mar 10 2014 EXAMPLE a(0) = 1^3 - 1^3 = 0; a(1) = (1+3)^3 - (1^3+3^3) = 64 - 28 = 36; a(2) = (1+3+5)^3 - (1^3+3^3+5^3) = 729 - 153 = 576; a(3) = (1+3+5+7)^3 - (1^3+3^3+5^3+7^3) = 4096 - 496 = 3600; a(4) = (1+3+5+7+9)^3 - (1^3+3^3+5^3+7^3+9^3) = 15625 - 1225 = 14400; etc. - Philippe Deléham, Mar 10 2014 MAPLE A099764:=n->n^2*(n+1)^2*(n+2)^2; seq(A099764(n), n=0..50); # Wesley Ivan Hurt, Mar 09 2014 MATHEMATICA Table[n^2*(n+1)^2*(n+2)^2, {n, 0, 50}] (* Vladimir Joseph Stephan Orlovsky, Apr 19 2011 *) Times@@@Partition[Range[0, 30]^2, 3, 1] (* Harvey P. Dale, Sep 02 2016 *) PROG (MAGMA) [n^2 * (n+1)^2 * (n+2)^2: n in [0..30]]; // Vincenzo Librandi, Oct 04 2011 CROSSREFS Cf. A001014, A002593. Sequence in context: A081447 A218311 A183356 * A003841 A226284 A223271 Adjacent sequences:  A099761 A099762 A099763 * A099765 A099766 A099767 KEYWORD easy,nonn AUTHOR Kari Lajunen (Kari.Lajunen(AT)Welho.com), Nov 11 2004 STATUS approved

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Last modified August 22 11:34 EDT 2019. Contains 326176 sequences. (Running on oeis4.)