A307996 Expansion of e.g.f. exp(1 - exp(x)*(1 - 2*x)).

1, 1, 4, 15, 73, 410, 2591, 18165, 139266, 1155509, 10293729, 97815520, 986113613, 10499247005, 117603042220, 1381191356979, 16958788930317, 217132031279842, 2892337840164051, 40002168264724193, 573363461815952802, 8502905138072937073, 130268705062115090965, 2058969680487762098496

Offset: 0

Author

Ilya Gutkovskiy, May 09 2019

Keywords

• nonn

Crossrefs

Cf. A000248, A000354, A003727, A005408, A275707.

Programs

Mathematica

nmax = 23; CoefficientList[Series[Exp[1 - Exp[x] (1 - 2 x)], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Sum[(2 k - 1) Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 23}]

Formula

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