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 A119771 Product of n^2 and n-th tetrahedral number: a(n) = n^3*(n+1)*(n+2)/6. 2
 0, 1, 16, 90, 320, 875, 2016, 4116, 7680, 13365, 22000, 34606, 52416, 76895, 109760, 153000, 208896, 280041, 369360, 480130, 616000, 781011, 979616, 1216700, 1497600, 1828125, 2214576, 2663766, 3183040, 3780295, 4464000, 5243216, 6127616, 7127505, 8253840 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS If n is divisible by 10, then a(n) is divisible by 1000. LINKS Table of n, a(n) for n=0..34. Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1). FORMULA From Alois P. Heinz, Feb 10 2023: (Start) a(n) = Sum_{k=0..n} k^2 * A061579(n,k). G.f.: x*(x+1)*(9*x+1)/(x-1)^6. (End) From Amiram Eldar, Feb 13 2023: (Start) Sum_{n>=1} 1/a(n) = 39/8 - 3*Pi^2/4 + 3*zeta(3). Sum_{n>=1} (-1)^(n+1)/a(n) = 12*log(2) - 51/8 - 3*Pi^2/8 + 9*zeta(3)/4. (End) EXAMPLE a(25) = n^3*(n+1)*(n+2)/6 = 25^3*(25+1)*(25+2)/6 = 15625*26*27/6 = 15625*13*9 = 1828125. MAPLE with(combinat):a:=n->sum(sum(sum(binomial(n+2, 2)/3, j=1..n), k=1..n), m=1..n): seq(a(n), n=0..31); # Zerinvary Lajos, May 30 2007 MATHEMATICA a[n_] := n^3*(n+1)*(n+2)/6; Array[a, 35, 0] (* Amiram Eldar, Feb 13 2023 *) CROSSREFS Cf. A000290, A000292, A061579. Sequence in context: A264531 A192129 A253131 * A055920 A055856 A195591 Adjacent sequences: A119768 A119769 A119770 * A119772 A119773 A119774 KEYWORD easy,nonn AUTHOR Brandon Ang (xyz1236(AT)verizon.net), Jun 28 2006 STATUS approved

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Last modified April 15 17:30 EDT 2024. Contains 371693 sequences. (Running on oeis4.)