This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A001801 M3001 N1216 #34 Apr 26 2025 08:06:29
%S A001801 3,15,105,315,6930,18018,90090,218790,2078505,4849845,22309287,
%T A001801 50702925,1825305300,4071834900,18032411700,39671305740,347123925225,
%U A001801 755505013725,3273855059475,7064634602025,121511715154830,260382246760350,1112542327066950,2370198870707850,20146690401016725
%N A001801 Coefficients of Legendre polynomials.
%D A001801 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.
%D A001801 G. Prévost, Tables de Fonctions Sphériques. Gauthier-Villars, Paris, 1933, pp. 156-157.
%D A001801 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001801 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001801 G. C. Greubel, <a href="/A001801/b001801.txt">Table of n, a(n) for n = 0..1000</a>
%H A001801 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H A001801 Milan Janjic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL12/Janjic/janjic22.html">Some classes of numbers and derivatives</a>, JIS 12 (2009) 09.8.3.
%F A001801 a(n) = 3*2^(n-3)*binomial(n + 3/2, n)*2^A011371(n+4). - _G. C. Greubel_, Apr 26 2025
%t A001801 A001801[n_]:= 3*2^(2*n+1)*Binomial[n+3/2, n]/2^DigitCount[n+4,2,1];
%t A001801 Table[A001801[n], {n,0,40}] (* _G. C. Greubel_, Apr 26 2025 *)
%o A001801 (PARI) a(n)=if(n<0,0,polcoeff(pollegendre(n+4),n)*2^valuation((n\2*2+4)!,2))
%o A001801 (Magma)
%o A001801 A001801:= func< n | 3*Binomial(n+3,3)*Catalan(n+2)*2^(Valuation(Factorial(n+4),2)-n-4) >;
%o A001801 [A001801(n): n in [0..30]]; // _G. C. Greubel_, Apr 26 2025
%o A001801 (SageMath)
%o A001801 def A001801(n): return 3*2^(n-3)*binomial(n+3/2,n)*2^valuation(factorial(n+4), 2)
%o A001801 print([A001801(n) for n in range(31)]) # _G. C. Greubel_, Apr 26 2025
%Y A001801 Cf. A001790, A001796, A008316, A011371.
%Y A001801 Bisection of A004733.
%Y A001801 Diagonal 3 of triangle A100258.
%K A001801 nonn
%O A001801 0,1
%A A001801 _N. J. A. Sloane_
%E A001801 More terms from _Michael Somos_, Oct 25 2002