A383409 Expansion of e.g.f. (exp(x)-1)*(exp(x)-x)*(exp(x)-x^2/2)*(exp(x)-x^3/6).
0, 1, 5, 19, 77, 326, 1406, 5601, 23715, 101092, 431172, 1841357, 7889877, 33924268, 146103678, 628595097, 2695143751, 11495831852, 48733234456, 205252231229, 858955851705, 3573016550756, 14781047390930, 60846099935609, 249385924540907
Offset: 0
Keywords
Examples
a(3)=19 since the strings are: 011 (3 of this type), 033 (3 of this type), 002 (3 of this type), 003 (3 of this type), 023 (6 of this type), and 000.
Crossrefs
Cf. A383323.
Formula
a(n) = 4^n - 3^n - n*(3^(n-1) - 2^(n-1)) - binomial(n,2)*(3^(n-2) - 2^(n-2)) - binomial(n,3)*(3^(n-3) - 2^(n-1) + 3) + binomial(n,4)*(2^(n-2) - 4) + 5*binomial(n,5)*(2^(n-4) - 2) - 60*binomial(n,6) except at n = 6.
Comments