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 A375655 #8 Aug 23 2024 02:13:05
%S A375655 1,1,3,10,37,186,931,5608,36345,252892,1961011,15811896,139137373,
%T A375655 1286591320,12584565267,130564271776,1410581283121,16095825151248,
%U A375655 190917669584035,2366869021623712,30550349329738581,408806590130340256,5688859328729212483
%N A375655 Expansion of e.g.f. exp(x^2 + x * exp(x^2/2)).
%F A375655 a(n) = n! * Sum_{k=0..floor(n/2)} ((n-2*k+2)/2)^k / (k! * (n-2*k)!).
%o A375655 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^2+x*exp(x^2/2))))
%o A375655 (PARI) a(n) = n!*sum(k=0, n\2, ((n-2*k+2)/2)^k/(k!*(n-2*k)!));
%Y A375655 Cf. A080108, A375656.
%Y A375655 Cf. A375633.
%K A375655 nonn
%O A375655 0,3
%A A375655 _Seiichi Manyama_, Aug 22 2024