A308876 Expansion of e.g.f. exp(x)*(1 - x)/(1 - 2*x).

1, 2, 7, 40, 317, 3166, 37987, 531812, 8508985, 153161722, 3063234431, 67391157472, 1617387779317, 42052082262230, 1177458303342427, 35323749100272796, 1130359971208729457, 38432239021096801522, 1383560604759484854775, 52575302980860424481432

Offset: 0

Author

Ilya Gutkovskiy, Jun 29 2019

Keywords

• nonn

Comments

Binomial transform of A002866.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..403

Crossrefs

Cf. A002866, A010844, A011782, A067273, A161936, A271705, A294466, A327606.

Row sums of A326659.

Programs

Maple

a:= n-> n! * add(ceil(2^(n-k-1))/k!, k=0..n):
seq(a(n), n=0..23);  # Alois P. Heinz, Sep 12 2019

Mathematica

nmax = 19; CoefficientList[Series[Exp[x] (1 - x)/(1 - 2 x), {x, 0, nmax}], x] Range[0, nmax]!
Table[1 + Sum[Binomial[n,k] 2^(k - 1) k!, {k, 1, n}], {n, 0, 19}]

Formula

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

a(n) = A010844(n) - A067273(n).

a(n) ~ n! * 2^(n-1) * exp(1/2). - Vaclav Kotesovec, Jun 29 2019

a(n) = Sum_{k=0..n} k! * A271705(n,k). - Alois P. Heinz, Sep 12 2019