A078298 Triangle of denominators of Integral_{x=0..1} LegendreP(m,x) * LegendreP(n,x) dx.

1, 2, 3, 1, 8, 5, 8, 1, 8, 7, 1, 48, 1, 128, 9, 16, 1, 128, 1, 128, 11, 1, 128, 1, 64, 1, 512, 13, 128, 1, 320, 1, 1536, 1, 512, 15, 1, 256, 1, 1024, 1, 2048, 1, 32768, 17, 256, 1, 1024, 1, 2048, 1, 32768, 1, 32768, 19, 1, 3072, 1, 7168, 1, 32768, 1, 24576, 1, 131072, 21

Offset

0,2

Links

Table of n, a(n) for n=0..65.

Eric Weisstein's World of Mathematics, Legendre Polynomial

Example

The triangle begins as:
   1;
   2,   3;
   1,   8,   5;
   8,   1,   8,   7;
   1,  48,   1, 128,   9;
  16,   1, 128,   1, 128,  11;
   1, 128,   1,  64,   1, 512, 13;
  ...

Prog

(PARI) T(m, n)=denominator(subst(intformal(pollegendre(m)*pollegendre(n)), 'x, 1))
for(n=0, 9, for(m=0, n, print1(T(m, n)", "))) \\ Charles R Greathouse IV, Mar 19 2017

Crossrefs

Cf. A078297.

Sequence in context: A331123 A182223 A011152 * A096063 A101281 A106033

Adjacent sequences: A078295 A078296 A078297 * A078299 A078300 A078301

Keyword

nonn,tabl,frac

Author

Eric W. Weisstein, Nov 21 2002

Status

approved