OFFSET
1,1
COMMENTS
5th partial summation within series as series accumulate n times from an initial sequence of Euler Triangle's row 3: 1,4,1.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube [Dead link]
C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube [Cached copy, May 15 2013]
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
G.f.: x*(6 - 6*x + x^2)/(1-x)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009; checked and corrected by R. J. Mathar, Sep 16 2009
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5), n > 5. - Harvey P. Dale, Nov 05 2011
E.g.f.: exp(x)*x*(144 + 144*x + 28*x^2 + x^3)/24. - Stefano Spezia, Oct 14 2022
MATHEMATICA
Table[25 n/12+(71n^2)/24+(11n^3)/12+n^4/24, {n, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {6, 24, 61, 125, 225}, 40] (* Harvey P. Dale, Nov 05 2011 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 18 2004
EXTENSIONS
Formula moved to be the definition by Eric M. Schmidt, Dec 12 2013
STATUS
approved