A186545 Sequence of coefficients arising in study of generating function for A067619.

1, -1, 3, -2, 5, -5, 8, -7, 13, -13, 18, -19, 26, -29, 39, -40, 52, -60, 72, -81, 101, -113, 134, -152, 181, -206, 243, -273, 318, -365, 418, -473, 549, -620, 710, -803, 914, -1034, 1177, -1322, 1498, -1691, 1904, -2139, 2416, -2704, 3036, -3400, 3811, -4261

Offset: 1

Author

N. J. A. Sloane, Feb 23 2011

Keywords

• sign

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..1000
• Arnold Knopfmacher and Neville Robbins, Identities for the total number of parts in partitions of integers, Util. Math. 67 (2005), 9-18. (See last line of text.)

Programs

Mathematica

nmax = 50; A067619 = CoefficientList[Series[Sum[k*x^(2*k - 1)*Product[1 + x^(2*j - 1), {j, 1, k - 1}], {k, 1, nmax + 1}], {x, 0, nmax + 1}], x]; A000700 = CoefficientList[Series[Product[1 + x^(2 k + 1), {k, 0, nmax + 1}], {x, 0, nmax + 1}], x]; b = ConstantArray[0, nmax + 1]; b[[1]] = 0; Do[b[[n + 1]] = (A067619[[n + 1]] - Sum[A000700[[n - k + 1]]*b[[k + 1]], {k, 0, n - 1}]) / A000700[[1]], {n, 1, nmax}]; Rest[b] (* Vaclav Kotesovec, Jun 28 2016 *)

Extensions

More terms from Vaclav Kotesovec, Jun 28 2016