A381307 - OEIS

%I #8 Feb 20 2025 08:39:50

%S 1,1,1,4,25,126,841,8303,84561,925480,12285121,181409427,2840445169,

%T 49113986936,932675641353,18883732449871,408771283327969,

%U 9499097097870720,234457146543484225,6115077874320445715,168654204908597822241,4902220448616467300248

%N E.g.f. A(x) satisfies A(x) = exp( x * cosh(x * A(x)^(1/2)) ).

%C As stated in the comment of A185951, A185951(n,0) = 0^n.

%F a(n) = Sum_{k=0..n} (n/2-k/2+1)^(k-1) * A185951(n,k).

%o (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));

%o a(n) = sum(k=0, n, (n/2-k/2+1)^(k-1)*a185951(n, k));

%Y Cf. A185951.

%K nonn,new

%O 0,4

%A _Seiichi Manyama_, Feb 19 2025