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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A048786 Triangle of coefficients of certain exponential convolution polynomials. 4
1, 8, 1, 96, 24, 1, 1536, 576, 48, 1, 30720, 15360, 1920, 80, 1, 737280, 460800, 76800, 4800, 120, 1, 20643840, 15482880, 3225600, 268800, 10080, 168, 1, 660602880, 578027520, 144506880, 15052800, 752640, 18816, 224, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

i) p(n,x) := sum(a(n,m)*x^m,m=1..n), p(0,x) := 1, are monic polynomials satisfying p(n,x+y)= sum(binomial(n,k)*p(k,x)*p(n-k,y),k=0..n), (exponential convolution polynomials). ii) In the terminology of the umbral calculus (see reference) p(n,x) are called associated to f(t)= t/(1+4*t). iii) a(n,1)= A034177(n).

Also the Bell transform of A034177. For the definition of the Bell transform see A264428. - Peter Luschny, Jan 28 2016

REFERENCES

S. Roman, The Umbral Calculus, Academic Press, New York, 1984

LINKS

Table of n, a(n) for n=1..36.

FORMULA

a(n, m) = n!*4^(n-m)*binomial(n-1, m-1)/m!, n >= m >= 1; a(n, m) := 0, m>n; a(n, m) = (n!/m!)*A038231(n-1, m-1) = 4^(n-m)*A008297(n, m) (Lah-triangle).

MAPLE

# The function BellMatrix is defined in A264428.

# Adds (1, 0, 0, 0, ..) as column 0.

BellMatrix(n -> 4^n*(n+1)!, 9); # Peter Luschny, Jan 28 2016

MATHEMATICA

rows = 8;

t = Table[4^n*(n+1)!, {n, 0, rows}];

T[n_, k_] := BellY[n, k, t];

Table[T[n, k], {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jun 22 2018, after Peter Luschny *)

CROSSREFS

Cf. A034177, A038231, A008297.

Sequence in context: A114152 A254933 A174503 * A240955 A132056 A051187

Adjacent sequences:  A048783 A048784 A048785 * A048787 A048788 A048789

KEYWORD

easy,nonn,tabl,changed

AUTHOR

Wolfdieter Lang

EXTENSIONS

T(8,4) corrected by Jean-François Alcover, Jun 22 2018

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 June 25 09:47 EDT 2018. Contains 311895 sequences. (Running on oeis4.)