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!)
 A292518 Expansion of Product_{k>=1} (1 - x^(k*(k+1)/2)). 8
 1, -1, 0, -1, 1, 0, -1, 1, 0, 1, -2, 1, 0, 1, -1, -1, 2, -1, 1, -2, 1, 0, 0, 0, 0, 1, -1, 1, -3, 2, -1, 2, -1, 0, 1, -1, 0, -2, 3, -1, 1, -2, 1, 1, -2, 0, 0, 2, 0, -1, 0, 2, -2, -1, -1, 1, 2, -1, 1, -1, 1, -2, 1, -2, 3, 1, -2, 0, -2, 3, -1, -1, 0, 3, -1, 0, -2, 1, 0, -3, 2, 2, 1, -1, -1, 0, 0, -1, 0, 2, -1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,11 COMMENTS Convolution inverse of A007294. The difference between the number of partitions of n into an even number of distinct triangular numbers and the number of partitions of n into an odd number of distinct triangular numbers. Euler transform of {-1 if n is a triangular number else 0, n > 0} = -A010054. - Gus Wiseman, Oct 22 2018 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 FORMULA G.f.: Product_{k>=1} (1 - x^(k*(k+1)/2)). MATHEMATICA nmax = 90; CoefficientList[Series[Product[1 - x^(k (k + 1)/2), {k, 1, nmax}], {x, 0, nmax}], x] CROSSREFS Product_{k>=1} (1 - x^(k*((m-2)*k-(m-4))/2)): this sequence (m=3), A276516 (m=4), A305355 (m=5). Cf. A007294, A010054, A024940, A280366, A320767, A320784. Sequence in context: A187360 A334368 A240718 * A264997 A222759 A024940 Adjacent sequences:  A292515 A292516 A292517 * A292519 A292520 A292521 KEYWORD sign AUTHOR Ilya Gutkovskiy, Sep 18 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 April 15 03:00 EDT 2021. Contains 342974 sequences. (Running on oeis4.)