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 A265021 Sum of fifth powers of the first n even numbers. 1
 0, 32, 1056, 8832, 41600, 141600, 390432, 928256, 1976832, 3866400, 7066400, 12220032, 20182656, 32064032, 49274400, 73574400, 107128832, 152564256, 213030432, 292265600, 394665600, 525356832, 690273056, 896236032, 1151040000, 1463540000, 1843744032 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Assoul Abdelkarim, The sums of powers of integers natural even, odd, RMSS-D-15-00105. Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1). FORMULA a(n) = 32 * Sum_{i=0..n} i^5 = (8/3)*n^2*(n+1)^2*(2*n^2+2*n-1). a(n) = 32 * A000539(n). G.f.: 32*x*(1 + 26*x + 66*x^2 + 26*x^3 + x^4)/(1-x)^7. - Vincenzo Librandi, Dec 01 2015 a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - Vincenzo Librandi, Dec 01 2015 EXAMPLE a(4) = 2^5 + 4^5 + 6^5 + 8^5 = 41600. MATHEMATICA Accumulate[Range[0, 60, 2]^5] (* Michael De Vlieger, Nov 30 2015 *) CoefficientList[Series[32 x (1 + 26 x + 66 x^2 + 26 x^3 + x^4)/(1 - x)^7, {x, 0, 33}], x] (* Vincenzo Librandi, Dec 01 2015 *) PROG (Magma) [(8/3)*n^2*(n+1)^2*(2*n^2+2*n-1): n in [0..30]]; // Vincenzo Librandi, Dec 01 2015 (PARI) vector(100, n, n--; (8/3)*n^2*(n+1)^2*(2*n^2+2*n-1)) \\ Altug Alkan, Dec 01 2015 CROSSREFS Cf. A000539, A002594 (the same for odd numbers). Sequence in context: A144319 A041481 A158685 * A159360 A249392 A114933 Adjacent sequences: A265018 A265019 A265020 * A265022 A265023 A265024 KEYWORD nonn AUTHOR Assoul Abdelkarim, Nov 30 2015 STATUS approved

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Last modified June 13 05:35 EDT 2024. Contains 373366 sequences. (Running on oeis4.)