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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A078341 Triangle read by rows: T(n,k) = n*T(n-1,k-1) + k*T(n-1,k) starting with T(0,0)=1. 1
1, 0, 1, 0, 1, 2, 0, 1, 7, 6, 0, 1, 18, 46, 24, 0, 1, 41, 228, 326, 120, 0, 1, 88, 930, 2672, 2556, 720, 0, 1, 183, 3406, 17198, 31484, 22212, 5040, 0, 1, 374, 11682, 96040, 295004, 385144, 212976, 40320, 0, 1, 757, 38412, 489298, 2339380, 4965900 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Triangle of coefficients of polynomials P[n]. Let F(t) satisfy dF/dt = exp(x*(exp(F)-1)) and F(0)=0. Then F(t) = Sum_{n>=0} P[n]/n! t^n, where P[n] is a polynomial in x of degree n-1. The constant term of the polynomial is zero for n >= 2. The coefficient of x is 1 for n >= 2. The coefficient of x^n in P[n+1] is n!. The value at 1 is given by sequence A007549.

LINKS

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

FORMULA

P[1]=1; P[n+1] = x*(d/dx)P[n] + x*n*P[n].

EXAMPLE

P[1]=1, P[2]=x, P[3]=x+2*x^2, P[4]=x+7*x^2+6*x^3, P[5]=x+18*x^2+46*x^3+24*x^4, P[6]=x+41*x^2+228*x^3+326*x^4+120*x^5.

Rows start 1; 0,1; 0,1,2; 0,1,7,6; 0,1,18,46,24; 0,1,41,228,326,120; ...

MAPLE

P[1] := 1; for n from 1 to 10 do P[n+1] := expand(x*diff(P[n], x)+x*n*P[n]) od;

MATHEMATICA

p[1][x_] = 1; p[n_][x_] := x*p[n-1]'[x] + x*(n-1)*p[n-1][x]; Table[ CoefficientList[ p[n][x], x], {n, 1, 10}] // Flatten (* Jean-Fran├žois Alcover, Jan 29 2013 *)

CROSSREFS

Cf. A007549, A000142.

Columns include A000007, A057427, A095151, A103768. Diagonals include A000142, A067318. Row sums are A007549.

Sequence in context: A101371 A154974 A291820 * A199459 A316649 A065329

Adjacent sequences:  A078338 A078339 A078340 * A078342 A078343 A078344

KEYWORD

easy,nonn,tabl

AUTHOR

F. Chapoton, Nov 22 2002

EXTENSIONS

Additional comments from Henry Bottomley, Feb 15 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 20 03:10 EDT 2019. Contains 323412 sequences. (Running on oeis4.)