A320939 a(n) = n! * [x^n] log(1 + Sum_{k>=1} k^n*x^k/k!).

0, 1, 3, 5, -650, -46071, 3121776, 5538166381, 3146076001776, -10459815889305231, -100694615309371571840, -193538025548431984737219, 38912028315765820944424730112, 2554132880645627969533690819801657, -106074951996903194289368162206783509504

Offset: 0

Author

Ilya Gutkovskiy, Oct 28 2018

Keywords

• sign

Comments

a(n) is the n-th term of the logarithmic transform of the n-th powers.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..77
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A009306, A033464, A279644, A300452.

Programs

Maple

seq(coeff(series(factorial(n)*log(1+add(k^n*x^k/factorial(k),k=1..n)),x,n+1), x, n), n = 0 .. 15); # Muniru A Asiru, Oct 28 2018

Mathematica

Table[n! SeriesCoefficient[Log[1 + Sum[k^n x^k/k!, {k, 1, n}]], {x, 0, n}], {n, 0, 14}]