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 A009210 #35 Dec 29 2024 21:41:09 %S A009210 1,1,1,-3,-15,-23,177,1253,1057,-37103,-245471,371085,15691665, %T A009210 76436089,-608056239,-10302629131,-20287425215,856245051169, %U A009210 8821231566145,-29959421725155,-1376333505095631,-7591883371988471,139148719952772849 %N A009210 Expansion of e.g.f.: exp(sin(x)*cos(x)). %H A009210 Vincenzo Librandi, <a href="/A009210/b009210.txt">Table of n, a(n) for n = 0..125</a> %F A009210 a(n) = Sum_{j=0..(n-1)/2} 2^(4*j-n+1)*(Sum_{i=0..(n-2*j)/2} (2*i+2*j-n)^n*binomial(n-2*j,i)*(-1)^(n-j-i))/(n-2*j)!, n>0, a(0)=1. - _Vladimir Kruchinin_, May 29 2011 %F A009210 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n-1,2*k) * (-4)^k * a(n-2*k-1). - _Ilya Gutkovskiy_, Feb 24 2022 %t A009210 With[{nn=30},CoefficientList[Series[Exp[Sin[x]*Cos[x]],{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Aug 10 2021 *) %o A009210 (Maxima) %o A009210 a(n):=sum((2^(4*j-n+1)*sum((2*i+2*j-n)^n*binomial(n-2*j,i)*(-1)^(n-j-i),i,0,((n-2*j)/2)))/(n-2*j)!,j,0,((n-1)/2)); /* _Vladimir Kruchinin_, May 29 2011 */ %o A009210 (PARI) x='x+O('x^66); Vec(serlaplace(exp(sin(x)*cos(x)))) /* _Joerg Arndt_, May 29 2011 */ %K A009210 sign,easy %O A009210 0,4 %A A009210 _R. H. Hardin_ %E A009210 Extended with signs by _Olivier Gérard_, Mar 15 1997 %E A009210 Definition corrected by _Joerg Arndt_, May 29 2011 %E A009210 Definition clarified and prior Mathematica program replaced by _Harvey P. Dale_, Aug 10 2021