A384201 Expansion of e.g.f. -log(1 - 2*x)/(2 * (1 + x)).

0, 1, 0, 8, 16, 304, 2016, 31968, 389376, 6817536, 117619200, 2422080000, 52684646400, 1277090150400, 33132492288000, 931341738700800, 27948405871411200, 896073058285977600, 30491347526251315200, 1099008249715585843200, 41796901408833994752000

Offset

0,4

Links

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

Formula

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

a(n) = -n * a(n-1) + 2^(n-1) * (n-1)!.

a(n) = (n-2) * a(n-1) + 2 * (n-1)^2 * a(n-2).

Prog

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

Crossrefs

Cf. A384202.

Sequence in context: A276978 A265094 A285060 * A371009 A369646 A061747

Adjacent sequences: A384198 A384199 A384200 * A384202 A384203 A384204

Keyword

nonn,easy

Author

Seiichi Manyama, May 22 2025

Status

approved