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.

A281432 E.g.f. C(x) satisfies: C(x) = cosh( Integral C(x)^5 dx ).

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%I A281432 #6 Mar 01 2017 10:54:51
%S A281432 1,1,21,1341,173961,38032281,12572222301,5853055718421,
%T A281432 3649908317290641,2936992590376253361,2962874009751302380581,
%U A281432 3662113951884448455886701,5442785335874229886957949721,9576772316393556595041389524041,19688717121629473508791582116311661,46766278604566476892923500929537926981,127098490344228968075529350992858163636001
%N A281432 E.g.f. C(x) satisfies: C(x) = cosh( Integral C(x)^5 dx ).
%F A281432 C(x)^2 - S(x)^2 = 1 and C(x) = 1 + Integral C(x)^5*S(x) dx, where S(x) is described by A281431.
%t A281432 terms = 20; max = 2terms; se = Series[(1/8)*((x*(5+3x^2))/(1+x^2)^2 + 3* ArcTan[x]), {x, 0, max}]; s[x_] = InverseSeries[se, x] // Normal; coes = CoefficientList[Sqrt[1+s[x]^2]+O[x]^(max+1), x]*Range[0, max]!; Partition[ coes, 2][[All, 1]] (* _Jean-François Alcover_, Mar 01 2017 *)
%o A281432 (PARI) {a(n) = my(S=x, C=1); for(i=0, n, S = intformal( C^6 +x*O(x^(2*n))); C = 1 + intformal( S*C^5 ) ); (2*n)!*polcoeff(C, 2*n)}
%o A281432 for(n=0, 30, print1(a(n), ", "))
%K A281432 nonn
%O A281432 0,3
%A A281432 _Paul D. Hanna_, Jan 21 2017