

A001795


Coefficients of Legendre polynomials.
(Formerly M4407 N1861)


6



1, 1, 7, 33, 715, 4199, 52003, 334305, 17678835, 119409675, 1641030105, 11435320455, 322476036831, 2295919134019, 32968493968795, 238436656380769, 27767032438524099, 203236010537432691, 2989949596465113373
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OFFSET

0,3


COMMENTS

Numerators in expansion of sqrt(c(x)), c(x) the g.f. of A000108.  Paul Barry, Jul 12 2005
Coefficient of Legendre_0(x) when x^n is written in term of Legendre polynomials.  Michel Marcus, May 28 2013


REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

T. D. Noe, Table of n, a(n) for n=0..100
H. E. Salzer, Coefficients for expressing the first twentyfour powers in terms of the Legendre polynomials, Math. Comp., 3 (1948), 1618.


FORMULA

1/(sqrt(1x)+sqrt(1+x)) = sum(n=0, inf, (a(n)/b(n))*x^(2n)) where b(n) is a power of 2.  Benoit Cloitre, Mar 12 2002
For n>=1, 2^(n+1)*a(2^(n1))=A001791(2^n). [Vladimir Shevelev, Sep 05 2010]


CROSSREFS

Divisor of A048990 and A065097. Apparently a bisection of A002596.
Bisection of A099024.
Cf. A000108, A001791.
Sequence in context: A202762 A202757 A266018 * A209897 A209814 A117663
Adjacent sequences: A001792 A001793 A001794 * A001796 A001797 A001798


KEYWORD

nonn


AUTHOR

N. J. A. Sloane.


EXTENSIONS

More terms from Benoit Cloitre, Mar 12 2002


STATUS

approved



