A332680 a(n) = -(-1)^n * n! * hypergeometric1F1(1 - n, 2, 4*n).

-1, 1, 6, 78, 1576, 43320, 1507824, 63549808, 3145681536, 178865283456, 11488065875200, 822528662774016, 64957295774721024, 5609010346397166592, 525718830294548330496, 53154054477553828608000, 5766597997397483718344704, 668177890990349738366042112, 82355042760252520538828242944

Offset: 0

Author

Vaclav Kotesovec, Feb 19 2020

Keywords

• sign

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..336

Crossrefs

Cf. A302112, A332679.

Programs

Mathematica

Table[-(-1)^n * n! * Hypergeometric1F1[1 - n, 2, 4*n], {n, 0, 20}]
Join[{-1}, Table[n! * Sum[(-1)^(n-k+1) * Binomial[n-1, k] * (4*n)^k / (k+1)!, {k, 0, n-1}], {n, 1, 20}]]

Formula

A302112(n) = (A332679(n) - 2*n*a(n)) * binomial(2*n, n) / 2^n.

a(n) ~ c * n^(n - 5/6) * exp(n), where c = Gamma(1/3) / (2^(11/6) * 3^(1/6) * sqrt(Pi)) = 0.3531663187295...