A293013 a(n) = n! * [x^n] exp(x/(1 - x)^n).

1, 1, 5, 55, 961, 24101, 818821, 36053515, 1984670465, 132825475081, 10583425959301, 988018789759871, 106673677280748865, 13172700275176482925, 1842428769970603518341, 289406832942160060794451, 50677793314733587473331201, 9829328870566195730521433105

Offset

0,3

Comments

Conjecture: a(n+k) == a(n) (mod k) for all n and k. If true, then for each k, the sequence a(n) taken modulo k is a periodic sequence and the period divides k. - Peter Bala, Mar 12 2023

Links

Seiichi Manyama, Table of n, a(n) for n = 0..274

Formula

a(n) = A293012(n,n).

Mathematica

Table[n! SeriesCoefficient[Exp[x/(1 - x)^n] , {x, 0, n}], {n, 0, 17}]

Crossrefs

Main diagonal of A293012. Cf. A361281.

Sequence in context: A141357 A357394 A093352 * A195513 A172493 A155807

Adjacent sequences: A293010 A293011 A293012 * A293014 A293015 A293016

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Sep 28 2017

Status

approved