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

1,5

Comments

Reversion of g.f. (with constant term omitted) for A010054.

Links

Table of n, a(n) for n=1..35.

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Series Reversion

Index entries for reversions of series

Formula

G.f. A(x) satisfies: Sum_{k>=1} A(x)^(k*(k+1)/2) = x.

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]]

Crossrefs

Cf. A006195, A010054, A179848, A259938.

Sequence in context: A113360 A089434 A268298 * A219512 A186695 A210587

Adjacent sequences: A291415 A291416 A291417 * A291419 A291420 A291421

Keyword

sign

Author

Ilya Gutkovskiy, Aug 23 2017

Status

approved