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 A166942 One fifth of product plus sum of five consecutive nonnegative numbers. 4
 2, 27, 148, 509, 1350, 3031, 6056, 11097, 19018, 30899, 48060, 72085, 104846, 148527, 205648, 279089, 372114, 488395, 632036, 807597, 1020118, 1275143, 1578744, 1937545, 2358746, 2850147, 3420172, 4077893, 4833054, 5696095 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS a(n) = ((n*...*(n+4))+(n+...+(n+4)))/5, n >= 0. Binomial transform of 2, 25, 96, 144, 96, 24, 0, 0, 0, 0, .... Partial sums of A062938 where initial term 1 is replaced by 2. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 FORMULA a(n) = (n^5 + 10n^4 + 35n^3 + 50n^2 + 29n + 10)/5. - Charles R Greathouse IV, Nov 02 2009 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) + 24 for n > 4; a(0)=2, a(1)=27, a(2)=148, a(3)=509, a(4)=1350. - Klaus Brockhaus, Nov 14 2009 G.f.: (2+15*x+16*x^2-14*x^3+6*x^4-x^5)/(1-x)^6. - Klaus Brockhaus, Nov 14 2009 EXAMPLE a(0) = (0*1*2*3*4 + 0 + 1 + 2 + 3 + 4)/5 = (0 + 10)/5 = 2. a(1) = (1*2*3*4*5 + 1 + 2 + 3 + 4 + 5)/5 = (120 + 15)/5 = 27. MATHEMATICA Table[((n+4)*(n+3)*(n+2)*(n+1)*n+(n+4)+(n+3)+(n+2)+(n+1)+n)/5, {n, 0, 100}] (Total[#]+Times@@#)/5&/@Partition[Range[0, 100], 5, 1]  (* Harvey P. Dale, Mar 05 2011 *) PROG (MAGMA) [ (&*s + &+s)/5 where s is [n..n+4]: n in [0..29] ]; // Klaus Brockhaus, Nov 14 2009 CROSSREFS Cf. A001477 (nonnegative integers), A062938 (squares of the form n(n+1)(n+2)(n+3)+1), A028387 (n+(n+1)^2), A167875, A166941, A166943. Sequence in context: A038625 A280089 A041801 * A119351 A098627 A263930 Adjacent sequences:  A166939 A166940 A166941 * A166943 A166944 A166945 KEYWORD nonn,easy AUTHOR Vladimir Joseph Stephan Orlovsky, Oct 24 2009 EXTENSIONS Edited and offset corrected by Klaus Brockhaus, Nov 14 2009 STATUS approved

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Last modified March 28 15:50 EDT 2020. Contains 333089 sequences. (Running on oeis4.)