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A001797 Coefficients of Legendre polynomials.

%I A001797 M2118 N0836 #27 Apr 25 2025 09:49:33
%S A001797 2,20,110,2600,16150,208012,1376550,74437200,511755750,7134913500,
%T A001797 50315410002,1433226830360,10292051290430,148889972762300,
%U A001797 1083802983548950,126935005433253024,933787075442258310,13799767368300523260
%N A001797 Coefficients of Legendre polynomials.
%C A001797 Coefficient of Legendre_2(x) when x^n is written in term of Legendre polynomials. - _Sean A. Irvine_, Nov 28 2012
%D A001797 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001797 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001797 G. C. Greubel, <a href="/A001797/b001797.txt">Table of n, a(n) for n = 1..830</a>
%H A001797 H. E. Salzer, <a href="http://dx.doi.org/10.1090/S0025-5718-1948-0023123-5">Coefficients for expressing the first twenty-four powers in terms of the Legendre polynomials</a>, Math. Comp., 3 (1948), 16-18.
%p A001797 a:=n->(10*n/((2*n+1)*(2*n+3)))*numer(binomial(4*n,2*n)/2^(4*n)); # _Sean A. Irvine_, Nov 28 2012
%t A001797 A001797[n_]:= With[{B=Binomial}, 20*B[n+1,2]*Numerator[B[4*n,2*n]/2^(4*n)]/( 3*B[2*n+3,3])];
%t A001797 Table[A001797[n], {n,30}] (* _G. C. Greubel_, Apr 23 2025 *)
%o A001797 (Magma)
%o A001797 B:= Binomial;
%o A001797 A001797:= func< n | 20*B(n+1,2)*Numerator(B(4*n,2*n)/2^(4*n))/(3*B(2*n+3,3)) >;
%o A001797 [A001797(n): n in [1..30]]; // _G. C. Greubel_, Apr 23 2025
%o A001797 (SageMath)
%o A001797 b=binomial
%o A001797 def A001797(n): return 20*b(n+1,2)*numerator(b(4*n,2*n)/2^(4*n))/(3*b(2*n+3,3))
%o A001797 print([A001797(n) for n in range(1,31)]) # _G. C. Greubel_, Apr 23 2025
%Y A001797 Cf. A001796.
%K A001797 nonn
%O A001797 1,1
%A A001797 _N. J. A. Sloane_
%E A001797 More terms from _Sean A. Irvine_, Nov 28 2012