A281267 Main diagonal of A276554.

1, -1, -3, 8, 13, -51, -120, 538, 781, -5419, -3053, 47673, 5080, -427740, 136462, 3922383, -3278067, -34819588, 48561567, 299316651, -603368637, -2509708844, 6948730643, 20210062532, -76150197416, -152569240051, 801154765564, 1039352472008, -8158396721266

Offset

0,3

Comments

From Peter Bala, Apr 18 2023: (Start)

The Gauss congruences a(n*p^k) == a(n*p^(k-1)) (mod p^k) hold for all primes p and all positive integers n and k.

Conjecture: the stronger supercongruences a(n*p^k) == a(n*p^(k-1)) (mod p^(2*k)) hold for all primes p >= 3 and all positive integers n and k. (End)

Links

Seiichi Manyama, Table of n, a(n) for n = 0..100

Formula

a(n) = [x^n] exp(-n*Sum_{k>=1} x^k/(k*(1 - x^k)^2)). - Ilya Gutkovskiy, May 30 2018

Mathematica

nmax = 40; Table[SeriesCoefficient[Product[(1 - x^k)^(n*k), {k, 1, n}], {x, 0, n}], {n, 0, nmax}] (* Vaclav Kotesovec, Apr 17 2017 *)

Crossrefs

Cf. A255672, A270922, A276554.

Sequence in context: A337504 A355240 A355514 * A346054 A153891 A056402

Adjacent sequences: A281264 A281265 A281266 * A281268 A281269 A281270

Keyword

sign

Author

Seiichi Manyama, Apr 13 2017

Status

approved