A354313 Expansion of e.g.f. 1/(1 - x/2 * (exp(2 * x) - 1)).

1, 0, 2, 6, 40, 280, 2496, 25424, 297984, 3920256, 57349120, 922611712, 16193375232, 307896882176, 6304666798080, 138318662000640, 3236895083167744, 80483201605795840, 2118875812456366080, 58882581280649117696, 1722441885524719042560

Offset

0,3

Links

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

Formula

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

a(n) = n! * Sum_{k=0..floor(n/2)} 2^(n-2*k) * k! * Stirling2(n-k,k)/(n-k)!.

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x/2*(exp(2*x)-1))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=2, i, j*2^(j-2)*binomial(i, j)*v[i-j+1])); v;
(PARI) a(n) = n!*sum(k=0, n\2, 2^(n-2*k)*k!*stirling(n-k, k, 2)/(n-k)!);

Crossrefs

Cf. A052848, A354314.

Cf. A216794, A353998, A354311.

Sequence in context: A264152 A333631 A337071 * A351739 A098854 A056787

Adjacent sequences: A354310 A354311 A354312 * A354314 A354315 A354316

Keyword

nonn

Author

Seiichi Manyama, May 23 2022

Status

approved