A156033 Numerator of (Sum_{k=1..n} k^3)/n!.

0, 1, 9, 6, 25, 15, 49, 7, 9, 5, 121, 11, 169, 91, 1, 1, 289, 17, 361, 19, 1, 11, 529, 23, 1, 13, 1, 1, 841, 29, 961, 31, 1, 17, 1, 1, 1369, 703, 1, 1, 1681, 41, 1849, 43, 1, 23, 2209, 47, 1, 1, 1, 1, 2809, 53, 1, 1, 1, 29, 3481, 59, 3721, 1891, 1, 1, 1, 1, 4489, 67, 1, 1, 5041, 71, 5329

Offset

0,3

References

V. Mangulis, Handbook of Series, Academic Press, 1965, p. 77.

Links

Table of n, a(n) for n=0..72.

Formula

Sum_{ n>=1 } x^n*(Sum_{k=1..n} k^3)/n! = x*exp(x)*(x^3+8*x^2+14*x+4)/4.

Example

0, 1, 9/2, 6, 25/6, 15/8, 49/80, 7/45, 9/280, 5/896, 121/145152, 11/100800, 169/13305600, ...

Crossrefs

Cf. A156034.

Sequence in context: A040074 A088999 A073782 * A196005 A196002 A370151

Adjacent sequences: A156030 A156031 A156032 * A156034 A156035 A156036

Keyword

nonn,frac

Author

N. J. A. Sloane, Oct 31 2009

Status

approved