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A004256
a(n) = n^2*(n+1)*(n+2)^2/6.
1
0, 3, 32, 150, 480, 1225, 2688, 5292, 9600, 16335, 26400, 40898, 61152, 88725, 125440, 173400, 235008, 312987, 410400, 530670, 677600, 855393, 1068672, 1322500, 1622400, 1974375, 2384928, 2861082
OFFSET
0,2
FORMULA
From Harvey P. Dale, May 26 2015: (Start)
G.f.: (3*x+14*x^2+3*x^3)/(x-1)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6); a(0)=0, a(1)=3, a(2)=32, a(3)=150, a(4)=480, a(5)=1225. (End)
From Amiram Eldar, Nov 02 2021: (Start)
Sum_{n>=1} 1/a(n) = 3/8.
Sum_{n>=1} (-1)^(n+1)/a(n) = 69/8 - 12*log(2). (End)
MATHEMATICA
Table[(n^2 (n+1)(n+2)^2)/6, {n, 0, 40}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 3, 32, 150, 480, 1225}, 40] (* Harvey P. Dale, May 26 2015 *)
PROG
(Magma) [n^2*(n+1)*(n+2)^2/6 : n in [0..50]]; // Wesley Ivan Hurt, Jan 22 2022
CROSSREFS
Equals (n+2) * A002417.
Sequence in context: A213845 A221464 A119940 * A183457 A322234 A264574
KEYWORD
nonn,easy
STATUS
approved