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 A369746 #14 Apr 14 2025 11:38:21
%S A369746 1,3,12,63,423,3528,35559,422901,5817744,91072269,1600588269,
%T A369746 31230827532,670252672593,15696888917427,398454496989012,
%U A369746 10899543418960167,319672849622745951,10007954229075765984,333139545206104991031,11749955670275356579941
%N A369746 Expansion of e.g.f. exp( 3 * (1-sqrt(1-2*x)) ).
%F A369746 a(0) = 1; a(n) = Sum_{k=0..n-1} 3^(n-k) * (n-1+k)! / (2^k * k! * (n-1-k)!).
%F A369746 a(n) = (2*n-3)*a(n-1) + 9*a(n-2).
%p A369746 # The row polynomials of A132062 evaluated at x = 3.
%p A369746 T := proc(n, k) option remember; if k = 0 then 0^n elif n < k then 0
%p A369746 else (2*(n - 1) - k)*T(n - 1, k) + T(n - 1, k - 1) fi end:
%p A369746 seq(add(T(n, k)*3^k, k = 0..n), n = 0..19); # _Peter Luschny_, Apr 25 2024
%t A369746 With[{nn=20},CoefficientList[Series[Exp[3(1-Sqrt[1-2x])],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Apr 14 2025 *)
%o A369746 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(3*(1-sqrt(1-2*x)))))
%Y A369746 Cf. A107104, A144301, A132062.
%Y A369746 Cf. A369722.
%K A369746 nonn
%O A369746 0,2
%A A369746 _Seiichi Manyama_, Jan 30 2024