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!)
A291451 Triangle read by rows, expansion of e.g.f. exp(x*(exp(z)/3 + 2*exp(-z/2)* cos(z*sqrt(3)/2)/3 - 1)), nonzero coefficients of z. 9
1, 0, 1, 0, 1, 10, 0, 1, 84, 280, 0, 1, 682, 9240, 15400, 0, 1, 5460, 260260, 1401400, 1401400, 0, 1, 43690, 7128576, 99379280, 285885600, 190590400, 0, 1, 349524, 193360720, 6600492080, 42549306800, 76045569600, 36212176000 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..35.

EXAMPLE

Triangle starts:

[1]

[0, 1]

[0, 1,    10]

[0, 1,    84,     280]

[0, 1,   682,    9240,    15400]

[0, 1,  5460,  260260,  1401400,   1401400]

[0, 1, 43690, 7128576, 99379280, 285885600, 190590400]

MAPLE

CL := (f, x) -> PolynomialTools:-CoefficientList(f, x):

A291451_row := proc(n) exp(x*(exp(z)/3+2*exp(-z/2)*cos(z*sqrt(3)/2)/3-1)):

series(%, z, 66): CL((3*n)!*coeff(series(%, z, 3*(n+1)), z, 3*n), x) end:

for n from 0 to 7 do A291451_row(n) od;

# Alternative:

A291451row := proc(n) local P; P := proc(m, n) option remember;

if n = 0 then 1 else add(binomial(m*n, m*k)*P(m, n-k)*x, k=1..n) fi end:

CL(P(3, n), x); seq(%[k+1]/k!, k=0..n) end: # Peter Luschny, Sep 03 2018

MATHEMATICA

P[m_, n_] := P[m, n] = If[n == 0, 1, Sum[Binomial[m*n, m*k]*P[m, n - k]*x, {k, 1, n}]];

row[n_] := Module[{cl = CoefficientList[P[3, n], x]}, Table[cl[[k + 1]]/k!, {k, 0, n}]];

Table[row[n], {n, 0, 7}] // Flatten (* Jean-Fran├žois Alcover, Jul 23 2019, after Peter Luschny *)

CROSSREFS

Cf. A048993 (m=1), A156289 (m=2), this seq. (m=3), A291452 (m=4).

Diagonal: A000012 (m=1), A001147 (m=2), A025035 (m=3), A025036 (m=4).

Row sums: A000110 (m=1), A005046 (m=2), A291973 (m=3), A291975 (m=4).

Alternating row sums: A000587 (m=1), A260884 (m=2), A291974 (m=3), A291976 (m=4).

Sequence in context: A038689 A030000 A221809 * A323836 A062520 A157962

Adjacent sequences:  A291448 A291449 A291450 * A291452 A291453 A291454

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Sep 07 2017

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 July 12 19:26 EDT 2020. Contains 335668 sequences. (Running on oeis4.)