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A001795
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Coefficients of Legendre polynomials.
(Formerly M4407 N1861)
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5
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1, 1, 7, 33, 715, 4199, 52003, 334305, 17678835, 119409675, 1641030105, 11435320455, 322476036831, 2295919134019, 32968493968795, 238436656380769, 27767032438524099, 203236010537432691, 2989949596465113373
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Numerators in expansion of sqrt(c(x)), c(x) the g.f. of A000108. - Paul Barry (pbarry(AT)wit.ie), Jul 12 2005
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REFERENCES
| H. E. Salzer, Coefficients for expressing the first twenty-four powers in terms of the Legendre polynomials, Math. Comp., 3 (1948), 16-18.
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).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
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FORMULA
| 1/(sqrt(1-x)+sqrt(1+x))=sum(n=0, inf, a(n)/b(n)*x^(2n)) where b(n) is a power of 2. - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 12 2002
For n>=1, 2^(n+1)*a(2^(n-1))=A001791(2^n). [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Sep 05 2010]
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CROSSREFS
| Divisor of A048990 and A065097. Apparently a bisection of A002596.
Bisection of A099024.
Sequence in context: A197565 A202762 A202757 * A117663 A063166 A195018
Adjacent sequences: A001792 A001793 A001794 * A001796 A001797 A001798
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 12 2002
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