A095891 Triangle read by rows: T(n,k) = (n-k+1)^(n-k+1), n>=1, 1<=k<=n.

1, 4, 1, 27, 4, 1, 256, 27, 4, 1, 3125, 256, 27, 4, 1, 46656, 3125, 256, 27, 4, 1, 823543, 46656, 3125, 256, 27, 4, 1, 16777216, 823543, 46656, 3125, 256, 27, 4, 1, 387420489, 16777216, 823543, 46656, 3125, 256, 27, 4, 1, 10000000000, 387420489, 16777216

Offset: 1

Author

Herman Jamke (hermanjamke(AT)fastmail.fm), Jul 10 2004

Keywords

• easy
• nonn
• tabl

Comments

Sequence B is called a reverse reluctant sequence of sequence A, if B is triangle array read by rows: row number k lists first k elements of the sequence A in reverse order. Sequence A095891 is reverse reluctant sequence of sequence A000312 (number of labeled mappings from n points to themselves (endofunctions): n^n). - Boris Putievskiy, Dec 14 2012

Links

• Herman Jamke and Boris Putievskiy (first 48 from Herman Jamke), Table of n, a(n) for n = 1..1000
• Boris Putievskiy, Transformations Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012.

Programs

Mathematica

#^#&/@Table[n-k+1,{n,10},{k,n}]//Flatten (* Harvey P. Dale, May 23 2021 *)

Formula

a(n) = A000312(m), where m=(t*t+3*t+4)/2-n, t=floor((-1+sqrt(8*n-7))/2) or ((t*t+3*t+4)/2-n)^((t*t+3*t+4)/2-n), where t=floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Dec 14 2012