A380035 E.g.f. A(x) satisfies A(x) = 1/sqrt( 1 - 2*x*exp(x*A(x)) ).

1, 1, 5, 42, 517, 8420, 171201, 4181128, 119339081, 3900501648, 143703797725, 5893732487456, 266358266633229, 13153210420876864, 704697559381904921, 40714369264722337920, 2523456287242464370321, 167019778198736205721856, 11757749450929277192860725

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

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

Prog

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

Crossrefs

Cf. A380015, A380042.

Sequence in context: A102693 A052654 A108398 * A370907 A239997 A102244

Adjacent sequences: A380032 A380033 A380034 * A380036 A380037 A380038

Keyword

nonn

Author

Seiichi Manyama, Jan 10 2025

Status

approved