A309472 a(n) = n^n - n * n!.

1, 0, 0, 9, 160, 2525, 42336, 788263, 16454656, 384154569, 9963712000, 284872585811, 8910352429056, 302794155321853, 11110786329481216, 437874275265339375, 18446409309071343616, 827234215200059132177, 39346292832569834471424, 1978417344403405821315979

Offset

0,4

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = A000312(n) - A001563(n).

E.g.f.: - x/(-1 + x)^2 + 1/(1 + W(-x)), where W(x) is the principal branch of Lambert's function. - Stefano Spezia, Sep 08 2019

Mathematica

Array[#^# - # #! &, 20] (* Michael De Vlieger, Sep 29 2019 *)

Prog

(PARI) a(n) = n^n - n*n!; \\ Michel Marcus, Aug 05 2019

Crossrefs

Cf. A000312, A001563.

Sequence in context: A230180 A361047 A360777 * A060348 A365016 A367163

Adjacent sequences: A309469 A309470 A309471 * A309473 A309474 A309475

Keyword

nonn,easy

Author

Francesco Scavello, Aug 04 2019

Status

approved