login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A076014 Triangle in which m-th entry of n-th row is m^(n-1). 2
1, 1, 2, 1, 4, 9, 1, 8, 27, 64, 1, 16, 81, 256, 625, 1, 32, 243, 1024, 3125, 7776, 1, 64, 729, 4096, 15625, 46656, 117649, 1, 128, 2187, 16384, 78125, 279936, 823543, 2097152, 1, 256, 6561, 65536, 390625, 1679616, 5764801, 16777216, 43046721 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

This becomes triangle A009998(n-1, m-1), n >= m >= 1, if the m-th column entries are divided by m^(m-1).

Row sums give A076015. The m-th column (without leading zeros) gives (m^(m-1)) powers of m, m >= 1.

T(n,m) is the number of functions f:[n-1]->[(n-1)m] such that f(x)=k*x for some positive integer k <= m. Since there exactly m choices for each of the (n-1) images under f, we obtain T(n,m) = m^(n-1). - Dennis P. Walsh, Feb 27 2013

T(n+1,m+1) = (m+1)^n is the number of partial functions from an n-element set to an m-element set, n >= m >= 0. - Mohammad K. Azarian, Jun 28 2021

LINKS

Table of n, a(n) for n=1..45.

FORMULA

T(n, m) = m^(n-1), n >= m >= 1, otherwise 0.

G.f. for m-th column: (m^(m-1))(x^m)/(1-m*x), m >= 1.

a(n,m) = Sum_{p=1..m} Stirling2(n,p)*A008279(m-1, p-1), n >= m >= 1, otherwise 0.

EXAMPLE

For example, T(3,2)=4 since there are exactly 4 functions f from {1,2} to {1,2,3,4} that satisfy f(x)=x or f(x)=2x. If we specify each function by the ordered pair (f(1),f(2)), the four functions are (1,2), (1,4), (2,2), and (2,4). - Dennis P. Walsh, Feb 27 2013

Triangle begins:

  1;

  1,   2;

  1,   4,    9;

  1,   8,   27,    64;

  1,  16,   81,   256,   625;

  1,  32,  243,  1024,  3125,   7776;

  1,  64,  729,  4096, 15625,  46656, 117649;

  1, 128, 2187, 16384, 78125, 279936, 823543, 2097152;

  ...

MAPLE

seq(seq(m^(n-1), m=1..n), n=1..20); # Dennis P. Walsh, Feb 27 2013

MATHEMATICA

Table[m^(n-1), {n, 10}, {m, n}]//Flatten (* Harvey P. Dale, May 27 2017 *)

CROSSREFS

Cf. A009998, A008279, A008277 (Stirling2).

Cf. A089072.

Sequence in context: A145864 A306392 A182739 * A120458 A183244 A086933

Adjacent sequences:  A076011 A076012 A076013 * A076015 A076016 A076017

KEYWORD

nonn,easy,tabl

AUTHOR

Wolfdieter Lang, Oct 02 2002

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 24 23:43 EDT 2022. Contains 356951 sequences. (Running on oeis4.)