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A001800 Coefficients of Legendre polynomials.
(Formerly M3123 N1266)
6
1, 3, 30, 70, 315, 693, 12012, 25740, 109395, 230945, 1939938, 4056234, 16900975, 35102025, 1163381400, 2404321560, 9917826435, 20419054425, 167890003050, 344616322050, 1412926920405, 2893136075115, 47342226683700, 96742811049300, 395033145117975 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
REFERENCES
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 798.
G. Prévost, Tables de Fonctions Sphériques. Gauthier-Villars, Paris, 1933, pp. 156-157.
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
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Eric Weisstein's World of Mathematics, Legendre Polynomial, eq. 28.
FORMULA
a(n) = (n+1) * C(2n+2, n+1) / 2^A000120(n+2).
MAPLE
wt:= proc(n) local m, r; m:=n; r:=0;
while m>0 do r:= r+irem(m, 2, 'm') od; r
end:
a:= n-> (n+1) *binomial(2*n+2, n+1)/2^wt(n+2):
seq(a(n), n=0..30); # Alois P. Heinz, May 29 2013
MATHEMATICA
a[n_] := (n+1)*Binomial[2*n+2, n+1]/2^DigitCount[n+2, 2, 1]; Table[a[n], {n, 0, 24}] (* Jean-François Alcover, Mar 13 2014 *)
PROG
(PARI) a(n)=if(n<0, 0, -polcoeff(pollegendre(n+2), n)*2^valuation((n\2*2)!, 2))
CROSSREFS
Cf. A001803.
Diagonal 2 of triangle A100258.
Sequence in context: A132084 A208880 A012009 * A152767 A195029 A211617
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Michael Somos, Oct 25 2002
STATUS
approved

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)