A167577 The second column of the ED3 array A167572.

1, 11, 83, 741, 8169, 106107, 1592235, 27062325, 514246545, 10798366635, 248374594755, 6209158112325, 167651197407225, 4861802228946075, 150717766502187675, 4973638859450709525, 174078640829054894625

Offset: 1

Author

Johannes W. Meijer, Nov 10 2009

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..150

Crossrefs

Equals the second column of the ED3 array A167572.

Other columns are A167576 and A167578.

Cf. A007509 and A025547 (the sum((-1)^(k+n)/(2*k+1), k=0..n-1) factor).

Programs

Mathematica

Table[(1/2)*(-1)^n*(2*n - 5)!!*((4*n^2 - 6*n - 2) + (16*n^3 - 24*n^2 - 4*n + 6)*Sum[(-1)^(k + n)/(2*k + 1), {k, 0, n - 1}]), {n, 1,50}] (* G. C. Greubel, Jun 16 2016 *)

Formula

a(n) = (1/2)*(-1)^n*(2*n-5)!!*((4*n^2-6*n-2)+(16*n^3-24*n^2-4*n+6)*sum((-1)^(k+n)/ (2*k+1), k=0..n-1)).