login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A033842 Triangle of coefficients of certain polynomials (exponents in decreasing order). 12
1, 1, 1, 3, 3, 1, 16, 16, 6, 1, 125, 125, 50, 10, 1, 1296, 1296, 540, 120, 15, 1, 16807, 16807, 7203, 1715, 245, 21, 1, 262144, 262144, 114688, 28672, 4480, 448, 28, 1, 4782969, 4782969, 2125764, 551124, 91854, 10206, 756, 36, 1, 100000000 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

See A049323.

LINKS

Table of n, a(n) for n=0..45.

W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

Thierry Lévy, The Number of Prefixes of Minimal Factorisations of a Cycle, The Electronic Journal of Combinatorics, 23(3) (2016), #P3.35

FORMULA

a(n, m) = binomial(n+1, m)*(n+1)^(n-m-1), n >= m >= 0 else 0.

EXAMPLE

{1}; {1,1}; {3,3,1}; {16,16,6,1}; {125,125,50,10,1}; .... E.g. third row {3,3,1} corresponds to polynomial p(2,x)= 3*x^2+3*x+1.

CROSSREFS

a(n, 0)= A000272(n+1), n >= 0 (first column), a(n, 1)= A000272(n+1), n >= 1 (second column). p(k-1, -x)/(1-k*x)^k = (-1+1/(1-k*x)^k)/(x*k^2) is for k=1..5 G.f. for A000012, A001792, A036068, A036070, A036083, respectively.

See also A049323.

Sequence in context: A105599 A239895 A106210 * A104417 A121438 A108391

Adjacent sequences:  A033839 A033840 A033841 * A033843 A033844 A033845

KEYWORD

easy,nonn,tabl

AUTHOR

Wolfdieter Lang

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 16 00:50 EDT 2018. Contains 316252 sequences. (Running on oeis4.)