cp's OEIS Frontend

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.

A009446 Expansion of e.g.f. sin(x*cos(x)) (odd powers only).

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%I A009446 #29 Jan 18 2025 09:09:36
%S A009446 1,-4,36,-848,23824,-871872,44942912,-2860930816,213856723200,
%T A009446 -19099352929280,2010469524579328,-242177953175506944,
%U A009446 32998102512641970176,-5069553933584348397568,870871673923373487243264,-165613871131289362192596992,34644281516790333651724337152
%N A009446 Expansion of e.g.f. sin(x*cos(x)) (odd powers only).
%H A009446 Robert Israel, <a href="/A009446/b009446.txt">Table of n, a(n) for n = 0..300</a>
%F A009446 a(n) = (-1)^n * Sum_{k=0..n} (binomial(2*n+1,2*k+1) * (Sum_{i=0..k} (2*k+1-2*i)^(2*n-2*k)*binomial(2*k+1,i)) / 2^(2*k)). - _Vladimir Kruchinin_, Jun 18 2011
%p A009446 S:= series(sin(x*cos(x)),x,60):
%p A009446 seq(coeff(S,x,i)*i!,i=1..59,2); # _Robert Israel_, Oct 09 2024
%t A009446 With[{nn=30},Take[CoefficientList[Series[Sin[x Cos[x]],{x,0,nn}],x] Range[0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, Oct 04 2017 *)
%o A009446 (Maxima) a(n):=(-1)^(n)*sum(binomial(2*n+1,2*k+1)*((sum((2*k+1-2*i)^(2*n-2*k)*binomial(2*k+1,i),i,0,((k)))))/(2^(2*k)),k,0,n); /* _Vladimir Kruchinin_, Jun 18 2011 */
%K A009446 sign
%O A009446 0,2
%A A009446 _R. H. Hardin_
%E A009446 Extended with signs by _Olivier Gérard_, Mar 15 1997