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 A176780 a(n) = n^4 + 6n^3 + 14n^2 + 15n + 6. 2
 6, 42, 156, 420, 930, 1806, 3192, 5256, 8190, 12210, 17556, 24492, 33306, 44310, 57840, 74256, 93942, 117306, 144780, 176820, 213906, 256542, 305256, 360600, 423150, 493506, 572292, 660156, 757770, 865830, 985056, 1116192, 1260006 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Essentially partial sums of A061804. Agrees with the known terms listed in A082986. Are the sequences identical? Partial sums of A061804 (see above comment) = 1*n^4 + 2*n^3 + 2*n^2 + 1*n^1. To obtain this sequence, all elements of which are pronic numbers of pronic number index number (e.g., a(8) = 8190 is the 90th pronic number and 90 is the 9th pronic number; 9 = 8 + 1), then switch n to (n+1). - Raphie Frank, Oct 17 2012 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA G.f.: 6*(1+x)^2/(1-x)^5. a(n) = 6*A006325(n+2). a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + 24; a(0)=6, a(1)=42, a(2)=156, a(3)=420. a(n) = a(-n-3). - Bruno Berselli, Sep 05 2011 MATHEMATICA Table[n^4+6n^3+14n^2+15n+6, {n, 0, 40}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {6, 42, 156, 420, 930}, 40] (* Harvey P. Dale, Mar 28 2012 *) PROG (Magma) [ n^4+6*n^3+14*n^2+15*n+6: n in [0..32] ]; (PARI) a(n)=n^4+6*n^3+14*n^2+15*n+6 \\ Charles R Greathouse IV, Oct 17 2012 (Python) def A176780(n): return n*(n*(n*(n + 6) + 14) + 15) + 6 # Chai Wah Wu, Aug 30 2022 CROSSREFS Cf. A061804 (2*n*(2*n^2+1)), A082986, A006325 (n*(n-1)*(n^2-n+1)/6), A176711, A176712. See A169938 for another version. Sequence in context: A046763 A199905 A360757 * A169938 A082986 A180806 Adjacent sequences: A176777 A176778 A176779 * A176781 A176782 A176783 KEYWORD nonn,easy AUTHOR Klaus Brockhaus, Apr 25 2010 STATUS approved

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Last modified June 17 07:23 EDT 2024. Contains 373433 sequences. (Running on oeis4.)