login
A272871
Imaginary part of (n + i)^4.
2
0, 0, 24, 96, 240, 480, 840, 1344, 2016, 2880, 3960, 5280, 6864, 8736, 10920, 13440, 16320, 19584, 23256, 27360, 31920, 36960, 42504, 48576, 55200, 62400, 70200, 78624, 87696, 97440, 107880, 119040, 130944, 143616, 157080, 171360, 186480, 202464, 219336
OFFSET
0,3
FORMULA
a(n) = 4*A007531(n+1).
a(n) = 4*(n-1)*n*(n+1).
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) for n>3.
G.f.: 24*x^2 / (1-x)^4.
a(n) = b(n+1)*b(n-1)-b(n)*b(n-2), where b(n) is A002378(n). - Anton Zakharov, Aug 15 2016
From Ilya Gutkovskiy, Aug 15 2016: (Start)
E.g.f.: 4*x^2*(3 + x)*exp(x).
a(n) = 24*binomial(n+1,3).
a(n) = Sum_{k=0..n} A064200(k). (End)
EXAMPLE
a(5) = 480 because (5 + i)^4 = 476 + 480*i.
MATHEMATICA
Table[Im[(n + I)^4], {n, 0, 38}] (* or *)
Table[4 (n - 1) n (n + 1), {n, 0, 38}] (* or *)
CoefficientList[Series[24 x^2/(1 - x)^4, {x, 0, 38}], x] (* Michael De Vlieger, May 08 2016 *)
PROG
(PARI) a(n) = 4*(n-1)*n*(n+1)
(PARI) vector(50, n, n--; imag((n+I)^4))
(PARI) concat(vector(2), Vec(24*x^2/(1-x)^4 + O(x^50)))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, May 08 2016
STATUS
approved