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A001796
Coefficients of Legendre polynomials.
(Formerly M3116 N1263)
0
1, 3, 27, 143, 3315, 20349, 260015, 1710855, 92116035, 631165425, 8775943605, 61750730457, 1755702867191, 12587970424449, 181858466731095, 1322239639929719, 154702037871777123, 1137023085979691001, 16789716964765636633
OFFSET
0,2
COMMENTS
Numerators in expansion of c(x)^(3/2), c(x) the g.f. of A000108. - Gerald McGarvey, Oct 07 2008
Coefficient of Legendre_1(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).
FORMULA
Numerators of g.f. ((1-sqrt(1-4*x))/(2*x))^(3/2). - Sean A. Irvine, Nov 27 2012
a(n) = numerator(3*binomial(2*n+1/2, n)/(2*n+3)). - Tani Akinari, Oct 31 2024
PROG
(PARI) my(x='x+O('x^30)); apply(numerator, Vec(((1-sqrt(1-4*x))/(2*x))^(3/2))) \\ Michel Marcus, Feb 04 2022
(PARI) a(n)=numerator(3*binomial(2*n+1/2, n)/(2*n+3)) \\ Tani Akinari, Oct 31 2024
CROSSREFS
Cf. A000108.
Sequence in context: A306442 A080424 A285008 * A174613 A341566 A354655
KEYWORD
nonn,changed
EXTENSIONS
More terms from Sean A. Irvine, Nov 27 2012
STATUS
approved