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A278073 Triangle read by rows, coefficients of the polynomials P(m, n) = Sum_{k=1..n} binomial(m*n, m*k)* P(m, n-k)*z with P(m, 0) = 1 and m = 3. 15
1, 0, 1, 0, 1, 20, 0, 1, 168, 1680, 0, 1, 1364, 55440, 369600, 0, 1, 10920, 1561560, 33633600, 168168000, 0, 1, 87380, 42771456, 2385102720, 34306272000, 137225088000, 0, 1, 699048, 1160164320, 158411809920, 5105916816000, 54752810112000, 182509367040000 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

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

FORMULA

E.g.f.: 1/(1-t*((1/3)*exp(x)+(2/3)*exp(-(1/2)*x)*cos((1/2)*x*sqrt(3))-1)), nonzero terms.

EXAMPLE

Triangle begins:

[1]

[0, 1]

[0, 1,    20]

[0, 1,   168,    1680]

[0, 1,  1364,   55440,   369600]

[0, 1, 10920, 1561560, 33633600, 168168000]

MAPLE

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:

for n from 0 to 6 do PolynomialTools:-CoefficientList(P(3, n), x) od;

# Alternatively:

A278073_row := proc(n)

1/(1-t*((1/3)*exp(x)+(2/3)*exp(-(1/2)*x)*cos((1/2)*x*sqrt(3))-1));

expand(series(%, x, 3*n+1)); (3*n)!*coeff(%, x, 3*n);

PolynomialTools:-CoefficientList(%, t) end:

for n from 0 to 6 do A278073_row(n) od;

MATHEMATICA

With[{m = 3}, Table[Expand[j!*SeriesCoefficient[1/(1 - t*(MittagLefflerE[m, x^m] - 1)), {x, 0, j}]], {j, 0, 21, m}]];

Function[arg, CoefficientList[arg, t]] /@ % // Flatten

CROSSREFS

Cf. A014606 (diagonal), A243664 (row sums), A002115 (alternating row sums), A281479 (central coefficients), A327023 (refinement).

Cf. A097805 (m=0), A131689 (m=1), A241171 (m=2), A278074 (m=4).

Sequence in context: A072840 A091234 A221873 * A324274 A070708 A200430

Adjacent sequences:  A278070 A278071 A278072 * A278074 A278075 A278076

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Jan 22 2017

STATUS

approved

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Last modified November 18 02:20 EST 2019. Contains 329243 sequences. (Running on oeis4.)