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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A109822 Triangle read by rows: T(n,1)=1, T(n,k)=T(n-1,k)+(n-1)T(n-1,k-1) for 1<=k<=n. 2
1, 1, 2, 1, 4, 6, 1, 7, 18, 24, 1, 11, 46, 96, 120, 1, 16, 101, 326, 600, 720, 1, 22, 197, 932, 2556, 4320, 5040, 1, 29, 351, 2311, 9080, 22212, 35280, 40320, 1, 37, 583, 5119, 27568, 94852, 212976, 322560, 362880, 1, 46, 916, 10366, 73639, 342964, 1066644 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

T(n,n)=n!. Sum of row n is the signless Stirling number of the first kind s(n,2)(A000254). T(n,k)=A096747(n,k) for 1<=k<=n.

LINKS

Table of n, a(n) for n=1..52.

FORMULA

T(n, k)=sum(|stirling1(n, n-i)|, i=0..k-1) for 1<=k<=n.

From Peter Bala, Jul 08 2012: (Start)

E.g.f.: x/(1-x)*{1/(1-x*z)^(1/x) - 1/(1-x*z)} = x*z + (x+2*x^2)*z^2/2! + (x+4*x^2+6*x^3)*z^3/3! + .... Cf. the e.g.f. of A059518.

(End)

EXAMPLE

T(5,3)=46 because 18+4*7=46.

Triangle begins:

*1......................1

*2...................1.....2

*3................1.....4.....6

*4.............1.....7....18....24

*5..........1....11....46....96...120

*6.......1....16...101...326...600...720

*7....1....22...197...932..2556..4320..5040

MAPLE

with(combinat): T:=(n, k)->add(abs(stirling1(n, n-i)), i=0..k-1): for n from 1 to 11 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form T:=proc(n, k) if k=1 then 1 elif k=n then n! else T(n-1, k)+(n-1)*T(n-1, k-1) fi end: for n from 1 to 11 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form. [Emeric Deutsch]

A109822_row := proc(n) local k, i;

add(add(abs(combinat[stirling1](n, n-i)), i=0..k)*x^(n-k-1), k=0..n-1);

seq(coeff(%, x, n-k), k=1..n) end:

seq(print(A109822_row(n)), n=1..7); # Peter Luschny, Sep 18 2011

CROSSREFS

Cf. A096747, A000254, A049444, A137650. A059518.

Sequence in context: A219142 A220226 A181854 * A274292 A114192 A114656

Adjacent sequences:  A109819 A109820 A109821 * A109823 A109824 A109825

KEYWORD

nonn,tabl

AUTHOR

Emeric Deutsch, Jul 03 2005

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 May 25 01:01 EDT 2017. Contains 287008 sequences.