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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 (* Jean-Fran├žois 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

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Last modified May 7 05:10 EDT 2021. Contains 343636 sequences. (Running on oeis4.)