login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A166960 Triangle T(n, k) read by rows: T(n, k)= (m*n-m*k+1)*T(n-1, k-1) + k*(m*k-(m-1))*T(n-1, k) where m = 1. 3
1, 1, 1, 1, 6, 1, 1, 27, 21, 1, 1, 112, 270, 58, 1, 1, 453, 2878, 1738, 141, 1, 1, 1818, 28167, 39320, 8739, 318, 1, 1, 7279, 264411, 769955, 375755, 37665, 685, 1, 1, 29124, 2430652, 13905746, 13243650, 2858960, 146560, 1434, 1, 1, 116505, 22108860 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

The general recursion relation T(n,k)= (m*n - m*k + 1)*T(n - 1, k - 1) + k*(m*k - (m - 1))*T(n - 1, k) connects several sequences for differing values of m. These are: m = 0 yields A008277, m = 1 yields this sequence, m = 2 yields A166961, and m = 3 yields A166962. These sequences are, in essence, generalized Stirling numbers of the second kind. - G. C. Greubel, May 29 2016

LINKS

G. C. Greubel, Table of n, a(n) for the first 25 rows

FORMULA

T(n, k) = (n-k+1)*T(n-1, k-1) + k^2*T(n-1, k).

EXAMPLE

Triangle starts:

{1},

{1, 1},

{1, 6, 1},

{1, 27, 21, 1},

{1, 112, 270, 58, 1},

{1, 453, 2878, 1738, 141, 1},

{1, 1818, 28167, 39320, 8739, 318, 1},

{1, 7279, 264411, 769955, 375755, 37665, 685, 1},

{1, 29124, 2430652, 13905746, 13243650, 2858960, 146560, 1434, 1},

{1, 116505, 22108860, 239506500, 414525726, 169140810, 18617280, 531456, 2949, 1}

...

MATHEMATICA

A[n_, 1] := 1; A[n_, n_] := 1; A[n_, k_] := (n - k + 1)*A[n - 1, k - 1] + k^2*A[n - 1, k]; Flatten[Table[A[n, k], {n, 10}, {k, n}]] (* modified by G. C. Greubel, May 29 2016 *)

T[ n_, k_] := Which[k < 1 || k > n, 0, 1 == k == n, 1, True, T[n, k] = k^2 T[n - 1, k] + (n - k + 1) T[n - 1, k - 1]]; (* Michael Somos, Apr 12 2019 *)

CROSSREFS

Cf. A008277, A166961, A166962.

Sequence in context: A035348 A140945 A141688 * A155908 A105373 A296548

Adjacent sequences:  A166957 A166958 A166959 * A166961 A166962 A166963

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Oct 25 2009

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 19 18:36 EDT 2021. Contains 347564 sequences. (Running on oeis4.)