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A001800
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Coefficients of Legendre polynomials.
(Formerly M3123 N1266)
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6
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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
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OFFSET
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0,2
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REFERENCES
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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).
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LINKS
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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].
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FORMULA
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a(n) = (n+1) * C(2n+2, n+1) / 2^A000120(n+2).
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MAPLE
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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):
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MATHEMATICA
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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 *)
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PROG
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(PARI) a(n)=if(n<0, 0, -polcoeff(pollegendre(n+2), n)*2^valuation((n\2*2)!, 2))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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