A168431 General number of transpositions of n objects with repetitions.

1, 2, 9, 46, 245, 1601

Offset

1,2

Links

Table of n, a(n) for n=1..6.

Formula

Apparently a(n)=A005651(n)-1, n>1. [From R. J. Mathar, Nov 26 2009]

Example

a(1)=1!/1!=1 because A035294(1)=1; a(2)=2!/(1!*1!)=2 because A035294(2)=1; a(3)=3!/(1!*1!*1!)+3!/(2!*1!)=9 because A035294(3)=2; a(4)=4!/(1!*1!*1!*1!)+4!/(2!*1!*1!)+4!/(2!*2!)+4!/(3!*1!)=46 because A035294(4)=4; a(5)=5!/(1!*1!*1!*1!*1!)+5!/(2!*1!*1!*1!)+5!/(2!*2!*1!)+5!/(3!*1!*1!)+5!/(3!*2!)+5!/(4!*1!)=245 because A035294(5)=6; a(6)=6!/(1!*1!*1!*1!*1!*1!)+6!/(2!*1!*1!*1!*1!)+6!/(2!*2!*1!*1!)+6!/(2!*2!*2!)+6!/(3!*1!*1!*1!)+6!/(3!*2!*1!)+6!/(3!*3!)+6!/(4!*1!*1!)+6!/(4!*2!)+6!/(5!*1!)=1601 because A035294(6)=10.

Crossrefs

Cf. A035294.

Cf. A036038. [From R. J. Mathar, Nov 26 2009]

Sequence in context: A251178 A162725 A268171 * A036726 A219197 A340942

Adjacent sequences: A168428 A168429 A168430 * A168432 A168433 A168434

Keyword

nonn

Author

Juri-Stepan Gerasimov, Nov 25 2009

Status

approved