A380954 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cosh(x * A(x)^(1/2)) / A(x) ).

1, 1, 0, 3, 12, 5, 240, 1477, 2688, 92241, 708480, 3249191, 99010560, 901895293, 7904053248, 228409722465, 2463665111040, 34395813683297, 972859311194112, 12562427535104683, 244985796671569920, 6929169035680039701, 108002308453438586880, 2673222017277309851453

Offset

0,4

Comments

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

Links

Table of n, a(n) for n=0..23.

Formula

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

Prog

(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));

Crossrefs

Cf. A185951.

Sequence in context: A009781 A266913 A381301 * A307027 A304566 A291156

Adjacent sequences: A380946 A380949 A380950 * A380955 A380956 A380957

Keyword

nonn,new

Author

Seiichi Manyama, Feb 19 2025

Status

approved