|
| |
| |
|
|
|
6, 24, 61, 125, 225, 371, 574, 846, 1200, 1650, 2211, 2899, 3731, 4725, 5900, 7276, 8874, 10716, 12825, 15225, 17941, 20999, 24426, 28250, 32500, 37206, 42399, 48111, 54375, 61225, 68696, 76824, 85646, 95200, 105525, 116661, 128649, 141531, 155350
(list; graph; refs; listen; history; internal format)
|
|
|
|
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. 5th row of the array shown in A101853.
|
|
|
LINKS
| Harvey P. Dale, Table of n, a(n) for n = 1..1000
C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube.
Index to sequences with linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
|
|
|
FORMULA
| a(n) = n*(n+1)*(n^2+21*n+50)/24.
G.f.: x*(6-6*x+x^2)/(1-x)^5. [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]
a(n)=5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5), n>5. [From Harvey P. Dale, Nov 05 2011]
|
|
|
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] (* From Harvey P. Dale, Nov 05 2011 *)
|
|
|
CROSSREFS
| Sequence in context: A160936 A007531 A130669 * A101877 A092348 A006528
Adjacent sequences: A101851 A101852 A101853 * A101855 A101856 A101857
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 18 2004
|
|
|
EXTENSIONS
| G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.
|
| |
|
|
