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

0,3

Links

Table of n, a(n) for n=0..20.

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)

Mathematica

f[n_] := 5^n*Sum[i^5/5^i, {i, n}]; Array[f, 30, 0]

Crossrefs

Cf. A000217, A047520, A066999, A067534. A008292.

Sequence in context: A232251 A232259 A232046 * A227825 A201609 A140847

Adjacent sequences: A218373 A218374 A218375 * A218377 A218378 A218379

Keyword

easy,nonn

Author

Robert G. Wilson v, Nov 28 2012

Status

approved