

A077070


Triangle read by rows: T(n,k) is the power of 2 in denominator of coefficients of Legendre polynomials, where n >= 0 and 0 <= k <= n.


2



0, 1, 1, 3, 2, 3, 4, 4, 4, 4, 7, 5, 6, 5, 7, 8, 8, 7, 7, 8, 8, 10, 9, 10, 8, 10, 9, 10, 11, 11, 11, 11, 11, 11, 11, 11, 15, 12, 13, 12, 14, 12, 13, 12, 15, 16, 16, 14, 14, 15, 15, 14, 14, 16, 16, 18, 17, 18, 15, 17, 16, 17, 15, 18, 17, 18, 19, 19, 19, 19, 18, 18, 18, 18, 19, 19, 19, 19, 22, 20, 21, 20, 22, 19, 20, 19, 22, 20, 21, 20, 22
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,4


LINKS

Table of n, a(n) for n=0..90.


EXAMPLE

Triangle T(n,k) (with rows n >= 0 and columns k >= 0) begins as follows:
0;
1, 1;
3, 2, 3;
4, 4, 4, 4;
7, 5, 6, 5, 7;
8, 8, 7, 7, 8, 8;
10, 9, 10, 8, 10, 9, 10;
...


MATHEMATICA

T[n_, k_] := IntegerExponent[Denominator[Coefficient[LegendreP[2n, x], x, 2k]], 2]; Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* JeanFrançois Alcover, Apr 28 2017 *)


PROG

(PARI) {T(n, k) = if( k<0  k>n, 0, valuation( polcoeff( pollegendre(2*n), 2*k), 2))}


CROSSREFS

Cf. A005187, A077071 (row sums).
A005187(n) = T(n, 0).
Sequence in context: A272886 A098822 A131597 * A075988 A029150 A255246
Adjacent sequences: A077067 A077068 A077069 * A077071 A077072 A077073


KEYWORD

nonn,tabl


AUTHOR

Michael Somos, Oct 25 2002


STATUS

approved



