A381383 - OEIS

%I #10 Feb 22 2025 09:55:46

%S 1,2,6,26,176,1842,25552,417146,7727232,162203810,3855123968,

%T 102712106202,3024863555584,97316416451282,3393616911181824,

%U 127581806046438074,5147059194652983296,221843071154521998402,10172731970828970557440,494451746675777509028762

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

%F E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381382.

%F a(n) = 2 * Sum_{k=0..n} k! * binomial(2*n-k+2,k)/(2*n-k+2) * A136630(n,k).

%o (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));

%o a(n) = 2*sum(k=0, n, k!*binomial(2*n-k+2, k)/(2*n-k+2)*a136630(n, k));

%Y Cf. A136630, A381382.

%K nonn,new

%O 0,2

%A _Seiichi Manyama_, Feb 22 2025