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 A101090 Third partial sums of fourth powers (A000583). 10
 1, 19, 135, 605, 2054, 5778, 14178, 31350, 63855, 121693, 219505, 378027, 625820, 1001300, 1555092, 2352732, 3477741, 5035095, 7155115, 9997801, 13757634, 18668870, 25011350, 33116850, 43375995, 56245761, 72257589, 92026135 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS In general, the r-th successive summation of the fourth powers from 1 to n = (2*n+r)*(12*n^2+12*n*r+r^2-5*r)*(r+n)!/((r+4)!*(n-1)!). Here r = 3. - Gary Detlefs, Mar 01 2013 LINKS FORMULA a(n) = (n*(1+n)*(2+n)*(3+n)*(3+2*n)*(-1+2*n*(3+n)))/840. G.f.: x*(1+x)*(1+10*x+x^2)/(1-x)^8. [Colin Barker, Apr 04 2012] a(n)= (2*n+3)*(12*n^2+36*n-6)*(n+3)!/(5040*(n-1)!), n>0 - Gary Detlefs, Mar 01 2013 CROSSREFS Cf. A101091, A101089. Sequence in context: A078977 A085464 A215863 * A213122 A211092 A142746 Adjacent sequences:  A101087 A101088 A101089 * A101091 A101092 A101093 KEYWORD easy,nonn AUTHOR Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 14 2004 EXTENSIONS Edited by Ralf Stephan, Dec 16 2004 STATUS approved

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Last modified August 22 20:40 EDT 2019. Contains 326188 sequences. (Running on oeis4.)