A291418 Expansion of the series reversion of Sum_{k>=1} x^(k*(k+1)/2).
1, 0, -1, 0, 3, -1, -12, 9, 55, -67, -267, 468, 1323, -3180, -6513, 21267, 30969, -140581, -135995, 919698, 494361, -5954217, -829116, 38113425, -9433359, -240844482, 154219912, 1499076989, -1585801575, -9161079266, 13958031252, 54710928759, -113373461193, -317030478360, 875491422246
Offset: 1
Keywords
Links
- N. J. A. Sloane, Transforms
- Eric Weisstein's World of Mathematics, Series Reversion
- Index entries for reversions of series
Programs
-
Mathematica
nmax = 35; Rest[CoefficientList[InverseSeries[Series[Sum[x^(k (k + 1)/2), {k, 1, nmax}], {x, 0, nmax}], x], x]] nmax = 35; Rest[CoefficientList[InverseSeries[Series[(-2 x^(1/8) + EllipticTheta[2, 0, Sqrt[x]])/(2 x^(1/8)), {x, 0, nmax}], x], x]]
Formula
G.f. A(x) satisfies: Sum_{k>=1} A(x)^(k*(k+1)/2) = x.
Comments