A381300 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cosh(x * A(x)^(1/2)) ).

1, 1, 2, 9, 60, 485, 4800, 57547, 804160, 12783969, 228447360, 4539156941, 99244045824, 2367795157741, 61230675251200, 1706241143585175, 50971847057326080, 1625178125581055297, 55087299146009640960, 1978201530490562626609, 75025096312729021972480

Offset: 0

Author

Seiichi Manyama, Feb 19 2025

Keywords

• nonn

Comments

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

Crossrefs

Cf. A185951.

Programs

PARI

a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = sum(k=0, n, k!*binomial(n/2+k/2+1, k)/(n/2+k/2+1)*a185951(n, k));

Formula

a(n) = Sum_{k=0..n} k! * binomial(n/2+k/2+1,k)/(n/2+k/2+1) * A185951(n,k).