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 A381346 #13 Apr 19 2025 05:54:25
%S A381346 1,1,2,8,40,244,1808,15632,154240,1712656,21132032,286800128,
%T A381346 4246266880,68108302144,1176458774528,21772909267712,429818456473600,
%U A381346 9015349812633856,200218257664704512,4693597812326094848,115820240623410872320,3000905720793597113344
%N A381346 Expansion of e.g.f. 1/( 1 - sinh(sqrt(2)*x) / sqrt(2) ).
%F A381346 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} 2^k * binomial(n,2*k+1) * a(n-2*k-1).
%F A381346 a(n) = Sum_{k=0..n} k! * 2^((n-k)/2) * A136630(n,k).
%F A381346 a(n) ~ sqrt(Pi/3) * 2^(n/2 + 1) * n^(n + 1/2) / (arcsinh(sqrt(2))^(n+1) * exp(n)). - _Vaclav Kotesovec_, Apr 19 2025
%o A381346 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381346 a(n) = sum(k=0, n, k!*2^((n-k)/2)*a136630(n, k));
%Y A381346 Cf. A191277, A381284, A381285, A381286, A381347.
%Y A381346 Cf. A136630.
%K A381346 nonn
%O A381346 0,3
%A A381346 _Seiichi Manyama_, Feb 20 2025