A101090 Third partial sums of fourth powers (A000583).

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

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

Paolo Xausa, Table of n, a(n) for n = 1..10000

C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube.

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

Mathematica

Nest[Accumulate, Range[50]^4, 3] (* Paolo Xausa, Jun 17 2024 *)

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