OFFSET
1,2
LINKS
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
KEYWORD
easy,nonn
AUTHOR
Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 14 2004
EXTENSIONS
Edited by Ralf Stephan, Dec 16 2004
STATUS
approved