A381448 - OEIS

%I #10 Feb 24 2025 05:40:16

%S 1,1,6,75,1464,39065,1324080,54460987,2635269504,146681897553,

%T 9233067686400,648538095601451,50289434320131072,4267083467872455529,

%U 393266542856236148736,39121731305087283953115,4178124995723585643970560,476806534212831941528989217,57905078072597558361906610176

%N E.g.f. A(x) satisfies A(x) = 1 + x*A(x)^3 * cosh(x*A(x)^3).

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

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

%F E.g.f.: ( (1/x) * Series_Reversion( x/(1 + x * cosh(x))^3 ) )^(1/3).

%F a(n) = (1/(3*n+1)) * Sum_{k=0..n} k! * binomial(3*n+1,k) * 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, k!*binomial(3*n+1, k)*a185951(n, k))/(3*n+1);

%Y Cf. A381171, A381447.

%Y Cf. A185951.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Feb 23 2025