A295100 a(n) = n! * [x^n] exp(n*x)/(1 - 2*x).

1, 3, 20, 201, 2688, 44815, 894528, 20792205, 551518208, 16438822587, 543934387200, 19783668211153, 784536321392640, 33689132092480839, 1557397919735103488, 77117362592836807125, 4072280214605427376128, 228441851811771488284915, 13566762607790788699226112, 850372121882700252639269337

Offset: 0

Author

Ilya Gutkovskiy, Nov 14 2017

Keywords

• nonn

Comments

The n-th term of the n-th binomial transform of A000165.

Links

• Robert Israel, Table of n, a(n) for n = 0..375
• N. J. A. Sloane, Transforms
• Index entries for sequences related to factorial numbers

Crossrefs

Cf. A000165, A010844, A063170, A082032, A295098, A295099.

Programs

Maple

S:= series(exp(n*x)/(1-2*x),x,51):
seq(n!*coeff(S,x,n),n=0..50); # Robert Israel, Nov 14 2017

Mathematica

Table[n! SeriesCoefficient[Exp[n x]/(1 - 2 x), {x, 0, n}], {n, 0, 19}]

Formula

a(n) ~ 2^n * exp(n/2) * n!. - Vaclav Kotesovec, Nov 14 2017

a(n) = n! * Sum_{k=0..n} n^k*2^(n-k)/k! = 2^n*Gamma(n+1, n/2)*exp(n/2). - Robert Israel, Nov 14 2017