A101091 Fourth partial sums of fourth powers (A000583).

1, 20, 155, 760, 2814, 8592, 22770, 54120, 117975, 239668, 459173, 837200, 1463020, 2464320, 4019412, 6372144, 9849885, 14884980, 22040095, 32037896, 45795530, 64464400, 89475750, 122592600, 165968595, 222214356, 294471945, 386498080

Offset

1,2

Links

Table of n, a(n) for n=1..28.

Cecilia Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube. [Dead link]

Cecilia Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube. [Cached copy, May 15 2013]

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

a(n) = n*(1 + n)*(2 + n)^2*(3 + n)*(4 + n)*(-1 + 3*n*(4 + n))/5040.

a(1)=1, a(2)=20, a(3)=155, a(4)=760, a(5)=2814, a(6)=8592, a(7)=22770, a(8)=54120, a(9)=117975, a(n)=9*a(n-1)-36*a(n-2)+84*a(n-3)- 126*a(n-4)+ 126*a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9). - Harvey P. Dale, Dec 30 2011

G.f.: x*(1+x)*(1+10*x+x^2)/(1-x)^9. - Colin Barker, Apr 04 2012

Sum_{n>=1} 1/a(n) = 3934693/3380 - 210*Pi^2/13 - (2268/13)*sqrt(3/13)*Pi*cot(sqrt(13/3)*Pi). - Amiram Eldar, Jan 26 2022

Mathematica

Nest[Accumulate, Range[30]^4, 4] (* or *) LinearRecurrence[ {9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 20, 155, 760, 2814, 8592, 22770, 54120, 117975}, 30] (* Harvey P. Dale, Dec 30 2011 *)

Crossrefs

Cf. A000583, A101090.

Sequence in context: A164605 A000492 A015866 * A120693 A120692 A324948

Adjacent sequences: A101088 A101089 A101090 * A101092 A101093 A101094

Keyword

easy,nonn

Author

Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 14 2004

Extensions

Edited by Ralf Stephan, Dec 16 2004

Status

approved