The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A101092 Second partial sums of fifth powers (A000584). 12
 1, 34, 310, 1610, 6035, 18236, 47244, 109020, 229845, 450670, 832546, 1463254, 2465255, 4005080, 6304280, 9652056, 14419689, 21076890, 30210190, 42543490, 58960891, 80531924, 108539300, 144509300, 190244925, 247861926, 319827834, 409004110, 518691535 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Luciano Ancora, Recurrence relation for the second partial sums of m-th powers Luciano Ancora, Second partial sums of the m-th powers 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 1. - N. J. A. Sloane, Mar 23 2014 (But beware of a typo) C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube [Dead link] C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube [Cached copy, May 15 2013] FORMULA a(n) = (n*(1 + n)*(2 + n)*(-1 + n*(2 + n))*(1 + 2*n*(2 + n)))/84. G.f.: x*(1 + 26*x + 66*x^2 + 26*x^3 + x^4)/(1-x)^8. - Colin Barker, Apr 16 2012 a(n) = Sum_{i=1..n} i*(n+1-i)^5, by the definition. - Bruno Berselli, Jan 31 2014 a(n) = 2*a(n-1) - a(n-2) + n^5. - Luciano Ancora, Jan 08 2015 MAPLE f:=n->(2*n^7-7*n^5+7*n^3-2*n)/84; [seq(f(n), n=0..50)];  # N. J. A. Sloane, Mar 23 2014 MATHEMATICA CoefficientList[Series[(1 + 26 x + 66 x^2 + 26 x^3 + x^4)/(1 - x)^8, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 24 2014 *) PROG (MAGMA) [(n*(1+n)*(2+n)*(-1+n*(2+n))*(1+2*n*(2+n)))/84: n in [1..40]]; // Vincenzo Librandi, Mar 24 2014 (Sage) [n*(1+n)*(2+n)*(n*(2+n)-1)*(1+2*n*(2+n))/84 for n in range(1, 30)] # Danny Rorabaugh, Apr 21 2015 (PARI) a(n)=n*(n+1)*(n+2)*(n*(n+2)-1)*(2*n*(2 + n)+1)/84 \\ Charles R Greathouse IV, Apr 21 2015 CROSSREFS Cf. A000539, A101099. Cf. A254640. Sequence in context: A230803 A209808 A160146 * A233061 A281805 A034978 Adjacent sequences:  A101089 A101090 A101091 * A101093 A101094 A101095 KEYWORD nonn,easy AUTHOR Cecilia Rossiter, Dec 14 2004 EXTENSIONS Edited by Ralf Stephan, Dec 16 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 19 00:04 EDT 2021. Contains 345125 sequences. (Running on oeis4.)