OFFSET
1,3
COMMENTS
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Steve Butler and Pavel Karasik, A note on nested sums, J. Int. Seq. (2010) Vol. 13, Issue 4, Art. No. 10.4.4. See p=5 in the last equation on page 3.
Sela Fried, Counting r X s rectangles in nondecreasing and Smirnov words, arXiv:2406.18923 [math.CO], 2024. See p. 9.
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
a(n) = (n+3)*(n+2)*(n+1)*n*(n-1)*(n-2)/48.
G.f.: 15*x^3 / (1-x)^7. - Colin Barker, Apr 18 2014
a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7) for n>7. - Wesley Ivan Hurt, Dec 03 2015
MAPLE
A240440:=n->(n+3)*(n+2)*(n+1)*n*(n-1)*(n-2)/48; seq(A240440(n), n=1..50); # Wesley Ivan Hurt, Apr 08 2014
MATHEMATICA
Table[(n+3)(n+2)(n+1)n(n-1)(n-2)/48, {n, 50}] (* Wesley Ivan Hurt, Apr 08 2014 *)
CoefficientList[Series[15 x^2/(1 - x)^7, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 19 2014 *)
PROG
(PARI) Vec(15*x^3/(1-x)^7 + O(x^100)) \\ Colin Barker, Apr 18 2014
(Magma) [(n+3)*(n+2)*(n+1)*n*(n-1)*(n-2)/48 : n in [1..50]]; // Wesley Ivan Hurt, Dec 03 2015
(PARI) vector(100, n, (n^2-1)*(n^2-4)*(n+3)*n/48) \\ Derek Orr, Dec 24 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Heinrich Ludwig, Apr 08 2014
STATUS
approved