# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a352638 Showing 1-1 of 1 %I A352638 #17 Mar 26 2022 13:41:09 %S A352638 1,3,18,159,1872,27543,486288,10016619,235798272,6244714443, %T A352638 183756215808,5947907121879,210026879004672,8034293365747743, %U A352638 330982609573398528,14609181655918083939,687820834029346947072,34407546247054875367443 %N A352638 Expansion of e.g.f. 1/(1 - 3*sin(x)). %F A352638 a(0) = 1; a(n) = 3 * Sum_{k=0..floor((n-1)/2)} (-1)^k * binomial(n,2*k+1) * a(n-2*k-1). %F A352638 a(n) ~ n! / (2^(3/2) * arcsin(1/3)^(n+1)). - _Vaclav Kotesovec_, Mar 26 2022 %t A352638 With[{m = 17}, Range[0, m]! * CoefficientList[Series[1/(1 - 3*Sin[x]), {x, 0, m}], x]] (* _Amiram Eldar_, Mar 26 2022 *) %o A352638 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*sin(x)))) %o A352638 (PARI) a(n) = if(n==0, 1, 3*sum(k=0, (n-1)\2, (-1)^k*binomial(n, 2*k+1)*a(n-2*k-1))); %Y A352638 Cf. A000111, A007289. %Y A352638 Cf. A107403, A352640. %K A352638 nonn %O A352638 0,2 %A A352638 _Seiichi Manyama_, Mar 25 2022 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE