A167578 The third column of the ED3 array A167572.

1, 17, 183, 2043, 26529, 398025, 6765975, 128556675, 2699661825, 62092533825, 1552309291575, 41912411683275, 1215458905032225, 37679245697871225, 1243414695550433175, 43519523831289457875, 1610222144582102522625

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 third column of the ED3 array A167572.

Other columns are A167576 and A167577.

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

Programs

Mathematica

Table[(1/4)*(-1)^(n)*(2*n - 7)!!*((8*n^4 - 20*n^3 - 22*n^2 + 55*n + 12) + (32*n^5 - 80*n^4 - 80*n^3 + 200*n^2 + 18*n - 45)*(Sum[(-1)^(k + n)/(2*k + 1), {k, 0, n - 1}])), {n, 1, 50}] (* G. C. Greubel, Jun 16 2016 *)

Formula

a(n) = (1/4)*(-1)^(n)*(2*n-7)!!*((8*n^4-20*n^3-22*n^2+55*n+12)+(32*n^5-80*n^4-80*n^3+200*n^2+18*n-45)*(sum((-1)^(k+n)/(2*k+1),k=0..n-1))).