A218376 a(n) = 5^n*sum_{i=1..n} i^5/5^i.
0, 1, 37, 428, 3164, 18945, 102501, 529312, 2679328, 13455689, 67378445, 337053276, 1685515212, 8427947353, 42140274589, 210702132320, 1053511710176, 5267559970737, 26337801743253, 131689011192364, 658445059161820
Offset: 0
Programs
-
Mathematica
f[n_] := 5^n*Sum[i^5/5^i, {i, n}]; Array[f, 30, 0]
Formula
From Peter Bala, Nov 29 2012: (Start)
a(n) = 1/512*(3535*5^n - (128*n^5 + 800*n^4 + 2400*n^3 + 4600*n^2 + 5700*n + 3535)).
Recurrence equation: a(n) = 5*a(n-1) + n^5.
G.f.: (x + 26*x^2 + 66*x^3 + 26*x^4 + x^5)/((1 - 5*x)*(1 - x)^6) = x + 37*x^2 + 428*x^3 + ....
(End)