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.

A009227 Expansion of e.g.f.: exp(sinh(x))/exp(x).

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%I A009227 #20 Apr 09 2022 20:29:16
%S A009227 1,0,0,1,0,1,10,1,56,281,246,4621,16412,53197,564642,1937937,13309648,
%T A009227 100397649,454215214,4082253589,26498068420,174791970677,
%U A009227 1575851086778,10628056916313,91523101970104,788580099169337,6237722665351750,60190551618214941
%N A009227 Expansion of e.g.f.: exp(sinh(x))/exp(x).
%C A009227 Number of partitions of n-set in which block sizes are odd and greater than 1. - _Vladeta Jovovic_, Aug 23 2007
%F A009227 a(0) = 1; a(n) = Sum_{k=1..floor((n-1)/2)} binomial(n-1,2*k) * a(n-2*k-1). - _Ilya Gutkovskiy_, Apr 09 2022
%p A009227 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A009227       binomial(n-1, 2*j)*a(n-2*j-1), j=1..(n-1)/2))
%p A009227     end:
%p A009227 seq(a(n), n=0..30);  # _Alois P. Heinz_, Apr 09 2022
%t A009227 With[{nn=30},CoefficientList[Series[Exp[Sinh[x]]/Exp[x],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jan 18 2015 *)
%o A009227 (PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(sinh(x))/exp(x))) \\ _Michel Marcus_, Apr 09 2022
%Y A009227 Cf. A003724, A009209.
%K A009227 nonn,easy
%O A009227 0,7
%A A009227 _R. H. Hardin_
%E A009227 Extended and signs tested by _Olivier Gérard_, Mar 15 1997
%E A009227 Definition clarified and prior Mathematica program replaced by _Harvey P. Dale_, Jan 18 2015