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 A381341 #10 Feb 21 2025 05:50:01
%S A381341 1,1,1,7,25,81,601,3207,18705,156385,1087441,8962823,84001897,
%T A381341 732712241,7487525865,78537490951,831722893217,9804469109953,
%U A381341 115549730623009,1431784628480007,18795444460125241,248964703826005777,3487888859183694329,50283005924345951111
%N A381341 Expansion of e.g.f. exp( x * cosh(sqrt(2)*x) ).
%C A381341 As stated in the comment of A185951, A185951(n,0) = 0^n.
%F A381341 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} 2^k * (2*k+1) * binomial(n-1,2*k) * a(n-2*k-1).
%F A381341 a(n) = Sum_{k=0..n} 2^((n-k)/2) * A185951(n,k).
%o A381341 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381341 a(n) = sum(k=0, n, 2^((n-k)/2)*a185951(n, k));
%Y A381341 Cf. A003727, A009189, A381273, A381274, A381275, A381276, A381342.
%Y A381341 Cf. A185951.
%K A381341 nonn
%O A381341 0,4
%A A381341 _Seiichi Manyama_, Feb 20 2025