The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A291418 Expansion of the series reversion of Sum_{k>=1} x^(k*(k+1)/2). 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Reversion of g.f. (with constant term omitted) for A010054. LINKS N. J. A. Sloane, Transforms Eric Weisstein's World of Mathematics, Series Reversion 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 26 08:06 EDT 2020. Contains 338027 sequences. (Running on oeis4.)