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 A351937 #12 Mar 28 2022 07:42:51 %S A351937 1,1,1,3,9,24,99,418,1769,9320,49541,278912,1764825,11319784,77850287, %T A351937 570610472,4290387409,34316005632,285335249065,2455224885440, %U A351937 22165590003849,206191758121856,1989511661589435,19903718061574144,204795484665487865,2179948112062667392 %N A351937 Expansion of e.g.f. exp( (sinh(x) + x*cosh(x)) / 2 ). %H A351937 Seiichi Manyama, <a href="/A351937/b351937.txt">Table of n, a(n) for n = 0..568</a> %F A351937 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n-1,2*k) * (k+1) * a(n-2*k-1). %t A351937 nmax = 25; CoefficientList[Series[Exp[(Sinh[x] + x Cosh[x])/2], {x, 0, nmax}], x] Range[0, nmax]! %t A351937 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, 2 k] (k + 1) a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 25}] %o A351937 (PARI) my(x='x+O('x^30)); Vec(serlaplace(exp((sinh(x) + x*cosh(x))/2))) \\ _Michel Marcus_, Feb 26 2022 %Y A351937 Cf. A000248, A003724, A003727, A349103, A349105. %K A351937 nonn %O A351937 0,4 %A A351937 _Ilya Gutkovskiy_, Feb 26 2022