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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 Alois P. Heinz, Table of n, a(n) for n = 0..500 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. A001790, A001801, A008316. Cf. A001803. Diagonal 2 of triangle A100258. Sequence in context: A132084 A208880 A012009 * A152767 A195029 A211617 Adjacent sequences: A001797 A001798 A001799 * A001801 A001802 A001803 KEYWORD nonn AUTHOR N. J. A. Sloane EXTENSIONS More terms from Michael Somos, Oct 25 2002 STATUS approved

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Last modified May 28 09:20 EDT 2023. Contains 362999 sequences. (Running on oeis4.)