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A268481 Triangle that arise in the study of Fekete polynomials. 0
1, -2, 10, 16, -184, 456, -272, 5776, -30736, 55504, 7936, -284288, 2555008, -8998016, 13801600, -353792, 20594432, -280444416, 1567885056, -4267790592, 5960135424, 22368256, -2093148160, 40551058432, -325702463488, 1337523883008, -3059655994368, 4024935613440 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..28.

Christian Günther, Kai-Uwe Schmidt, Lq norms of Fekete and related polynomials, arXiv:1602.01750 [math.NT], 2016.

EXAMPLE

First few rows are:

1;

-2, 10;

16, -184, 456;

-272, 5776, -30736, 55504;

7936, -284288, 2555008, -8998016, 13801600;

...

MATHEMATICA

T[k_] := T[k] = 1 - Sum[Binomial[2k-1, 2j-1] T[j], {j, 1, k-1}];

eul[n_, x_] := Sum[(-1)^j Binomial[n+1, j] (x-j+1)^n, {j, 0, x+1}];

F[k_, m_] := F[k, m] = If[k == 0 && m == 0, 1, Sum[Binomial[2k-1, 2j-1] T[j] Sum[eul[2j-1, i-1] F[k-j, m-i], {i, 1, m}]/(2j-1)!, {j, 1, k}]];

Table[(2n-1)! F[n, k], {n, 1, 7}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 27 2018, from PARI *)

PROG

(PARI) T(k) = {my(j); 1 - sum(j=1, k-1, binomial(2*k-1, 2*j-1)*T(j))};

eul(n, x) = {my(j); sum(j=0, x+1, (-1)^j*binomial(n+1, j)*(x+1-j)^n)};

F(k, m) = if ((k==0) && (m==0), 1, sum(j=1, k, binomial(2*k-1, 2*j-1)*T(j)*sum(i=1, m, eul(2*j-1, i-1)*F(k-j, m-i))/(2*j-1)!));

tabl(nn) = for (n=1, nn, for (k=1, n, print1((2*n-1)!*F(n, k), ", ")); print(); );

CROSSREFS

Cf. A000182 (first column unsigned), A008292 (Eulerian numbers).

Sequence in context: A131474 A249153 A276046 * A009387 A305093 A316753

Adjacent sequences:  A268478 A268479 A268480 * A268482 A268483 A268484

KEYWORD

sign,tabl

AUTHOR

Michel Marcus, Feb 05 2016

STATUS

approved

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Last modified July 31 17:15 EDT 2021. Contains 346376 sequences. (Running on oeis4.)