A129587 a(n) = n!*((1 + 3n + n^2)*H(n) - n), where H(n) is the n-th harmonic number.

4, 29, 191, 1354, 10634, 92700, 892548, 9430416, 108630864, 1356063840, 18245210400, 263298142080, 4057825368960, 66527793642240, 1156298057913600, 21239191491840000, 411134620109875200, 8365635747476582400

Offset

1,1

Comments

The numbers can be generated from row sums from coefficients of the polynomials Sum_{i=1..n} ((n+1)^2 - 1 + (n+1-i)*z^n)*z^(i-1)/i.

The coefficients written as an array of 2n numbers in row n for the first 5 polynomials are

3 1 <- 3+z

8 4 2 1/2 <- 8+4z+2z^2+z^3/2

15 15/2 5 3 1 1/3

24 12 8 6 4 3/2 2/3 1/4

35 35/2 35/3 35/4 7 5 2 1 1/2 1/5

These rows multiplied by n! are

3 1

16 8 4 1

90 45 30 18 6 2

576 288 192 144 96 36 16 6

4200 2100 1400 1050 840 600 240 120 60 24

where the first column is A129326. The latter row sums define a(n), which are n! times the polynomials evaluated at z=1.

Links

Table of n, a(n) for n=1..18.

Crossrefs

Cf. A001008, A002805, A129326.

Sequence in context: A079885 A364404 A121191 * A143551 A288913 A100022

Adjacent sequences: A129584 A129585 A129586 * A129588 A129589 A129590

Keyword

nonn,less

Author

Paul Curtz, May 30 2007

Extensions

Edited and corrected by R. J. Mathar, Jul 27 2008

Status

approved