A371045 E.g.f. satisfies A(x) = 1 + x^3*A(x)*exp(x*A(x)).

1, 0, 0, 6, 24, 60, 840, 15330, 161616, 1572984, 29031120, 636008670, 11426850600, 210095235636, 5137568918664, 139255673359530, 3574532174656800, 95923063388359920, 2974073508961556256, 98747639807081454774, 3287535337205171488440

Offset

0,4

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} k^(n-3*k) * binomial(n-2*k+1,k)/( (n-2*k+1)*(n-3*k)! ).

Prog

(PARI) a(n) = n!*sum(k=0, n\3, k^(n-3*k)*binomial(n-2*k+1, k)/((n-2*k+1)*(n-3*k)!));

Crossrefs

Cf. A370985, A371019, A371044, A371046.

Cf. A365285.

Sequence in context: A366546 A272951 A358081 * A371159 A371199 A362703

Adjacent sequences: A371042 A371043 A371044 * A371046 A371047 A371048

Keyword

nonn

Author

Seiichi Manyama, Mar 09 2024

Status

approved