OFFSET
0,2
COMMENTS
Sum of n terms of the arithmetic progression with first term 1 and common difference n-1. - Amarnath Murthy, Aug 04 2005
a(n) is the sum of (n+1)-th row terms of triangle A144693. - Gary W. Adamson, Sep 19 2008
See also A131685(k) = smallest positive number m such that c(i) = m*(i^1 + 1)*(i^2 + 2)* ... *(i^k+ k) / k! takes integral values for all i>=0: For k=2, A131685(k)=1, which implies that this is a well-defined integer sequence. - Alexander R. Povolotsky, Apr 24 2015
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..1000
Justin Crum, Cyrus Cheng, David A. Ham, Lawrence Mitchell, Robert C. Kirby, Joshua A. Levine, and Andrew Gillette, Bringing Trimmed Serendipity Methods to Computational Practice in Firedrake, arXiv:2104.12986 [math.NA], 2021.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = (n+1)*(n^2 + 2)/2.
From Paul Barry, Nov 18 2005: (Start)
a(n) = Sum_{k=0..n} Sum_{j=0..n} (k-(k-1)*C(0, j-k)).
G.f.: (1 - x + 3x^2)/(1 - x)^4. - R. J. Mathar, Jul 07 2009
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Wesley Ivan Hurt, Feb 21 2015
a(n) = A057145(n+2,n+1). - R. J. Mathar, Jul 28 2016
MAPLE
MATHEMATICA
Table[(n + 1) (n^2 + 2)/2, {n, 0, 50}] (* Wesley Ivan Hurt, Feb 21 2015 *)
PROG
(PARI) { for (n=0, 1000, write("b064808.txt", n, " ", (n + 1)*(n^2 + 2)/2) ) } \\ Harry J. Smith, Sep 26 2009
(Magma) [(n+1)*(n^2+2)/2 : n in [0..50]]; // Wesley Ivan Hurt, Feb 21 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Floor van Lamoen, Oct 22 2001
STATUS
approved