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A215518 2n-th derivative of cosh(x)^cosh(x) at x=0.

%I A215518 #30 Apr 14 2023 14:04:03
%S A215518 1,1,7,76,1597,41776,1673167,74527636,4832747017,305644428256,
%T A215518 30618856073947,2276081971574236,390042814538656957,
%U A215518 20435946140834126176,10544180964356207226247,-604793906292405974180324,688972694565220644332739217,-181007844268190205159712489664
%N A215518 2n-th derivative of cosh(x)^cosh(x) at x=0.
%H A215518 Seiichi Manyama, <a href="/A215518/b215518.txt">Table of n, a(n) for n = 0..243</a>
%F A215518 From _Seiichi Manyama_, Aug 17 2022: (Start)
%F A215518 a(0) = 1; a(n) = Sum_{k=1..n} A354520(2*k) * binomial(2*n-1,2*k-1) * a(n-k).
%F A215518 a(n) = (-1)^n * A215515(n). (End)
%p A215518 a:= n-> coeff(series(cosh(x)^cosh(x), x, 2*n+1), x, 2*n)*(2*n)!:
%p A215518 seq(a(n), n=0..21);  # _Alois P. Heinz_, Aug 15 2012, revised, Apr 14 2023
%t A215518 f[x_] := Cosh[x]^Cosh[x]; Table[Derivative[2*n][f][0],{n,0,30}]
%o A215518 (PARI) a354520(n) = sum(k=1, n\2, (16^k-4^k)*bernfrac(2*k)/(2*k)*binomial(n, 2*k));
%o A215518 a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a354520(2*j)*binomial(2*i-1, 2*j-1)*v[i-j+1])); v; \\ _Seiichi Manyama_, Aug 17 2022
%Y A215518 Cf. A000182, A215515, A354518, A354520.
%K A215518 sign
%O A215518 0,3
%A A215518 _Michel Lagneau_, Aug 14 2012