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 A145216 Self-convolution of (1^3, 2^3, 3^3, 4^3, ... ). 4
 1, 16, 118, 560, 2003, 5888, 14988, 34176, 71445, 139216, 255970, 448240, 752999, 1220480, 1917464, 2931072, 4373097, 6384912, 9142990, 12865072, 17817019, 24320384, 32760740, 43596800, 57370365, 74717136, 96378426, 123213808 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row sums of A098360. - N. J. A. Sloane, May 31 2009 REFERENCES A. Umar, B. Yushau and B. M. Ghandi, (2006), "Patterns in convolution of two series", in Stewart, S. M., Olearski, J. E. and Thompson, D. (Eds), Proceedings of the Second Annual Conference for Middle East Teachers of Science, Mathematics and Computing (pp. 95-101). METSMaC: Abu Dhabi. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 C. P. Neuman and D. I. Schonbach, Evaluation of sums of convolved powers using Bernoulli numbers, SIAM Rev. 19 (1977), no. 1, 90--99. MR0428678 (55 #1698). See Table 2. - N. J. A. Sloane, Mar 23 2014 A. Umar, B. Yushau and B. M. Ghandi, Convolution of two series, Australian Senior Maths Journal 21(2) (2007), 6-11. FORMULA a(n) = C(n+2,3)*(3*n*(n+2)*(n^2+2*n+3)+16)/70. G.f.: x*(1+4*x+x^2)^2/(1-x)^8. [Joerg Arndt, Jun 18 2012] EXAMPLE a(3) = 118 because 1*(3^3) + (2^3)*(2^3) + (3^3)*1 = 118. MAPLE f:=n->(3*n^7+7*n^3-10*n)/420; [seq(f(n), n=0..50)];  # N. J. A. Sloane, Mar 23 2014 MATHEMATICA Table[Sum[(k - i)^3 (1 + i)^3, {i, 0, k - 1}], {k, 1, 35}] (* Clark Kimberling, Jun 17 2012 *) CoefficientList[Series[(1 + 4 x + x^2)^2/(1 - x)^8, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 24 2014 *) PROG (MAGMA) [(3*n^7+7*n^3-10*n)/420: n in [2..40]]; // Vincenzo Librandi, Mar 24 2014 CROSSREFS Cf. A098360. Sequence in context: A279163 A101377 A302897 * A200173 A226761 A250169 Adjacent sequences:  A145213 A145214 A145215 * A145217 A145218 A145219 KEYWORD nonn AUTHOR Abdullahi Umar, Oct 05 2008 EXTENSIONS Name corrected by Clark Kimberling, Jun 17 2012 STATUS approved

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Last modified June 20 04:43 EDT 2021. Contains 345157 sequences. (Running on oeis4.)