This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A101090 #25 Aug 21 2025 03:28:28 %S A101090 1,19,135,605,2054,5778,14178,31350,63855,121693,219505,378027,625820, %T A101090 1001300,1555092,2352732,3477741,5035095,7155115,9997801,13757634, %U A101090 18668870,25011350,33116850,43375995,56245761,72257589,92026135,116258680,145765224,181469288 %N A101090 Third partial sums of fourth powers (A000583). %C A101090 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 %H A101090 Paolo Xausa, <a href="/A101090/b101090.txt">Table of n, a(n) for n = 1..10000</a> %F A101090 a(n) = (n*(1+n)*(2+n)*(3+n)*(3+2*n)*(-1+2*n*(3+n)))/840. %F A101090 G.f.: x*(1+x)*(1+10*x+x^2)/(1-x)^8. - _Colin Barker_, Apr 04 2012 %F A101090 a(n) = (2*n+3)*(12*n^2+36*n-6)*(n+3)!/(5040*(n-1)!). - _Gary Detlefs_, Mar 01 2013 %t A101090 Nest[Accumulate, Range[50]^4, 3] (* _Paolo Xausa_, Jun 17 2024 *) %Y A101090 Cf. A101091, A101089. %K A101090 easy,nonn %O A101090 1,2 %A A101090 Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 14 2004 %E A101090 Edited by _Ralf Stephan_, Dec 16 2004