A193933 E.g.f. A(x) = exp(x+x^2+x^3+x^4+x^5+x^6+x^7).

1, 1, 3, 13, 73, 501, 4051, 37633, 354033, 3870793, 46240291, 597877941, 8298856633, 122751616573, 1921371570483, 31604885804521, 552755907700321, 10156326950561553, 195421314725788483, 3926668816722630493, 82199760488718697641, 1789438454541407131141

Offset: 0

Author

Vladimir Kruchinin, Aug 09 2011

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..476

Crossrefs

Column k=7 of A293669.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      a(n-j)*binomial(n-1, j-1)*j!, j=1..min(n, 7)))
    end:
seq(a(n), n=0..23);  # Alois P. Heinz, Sep 29 2017

Mathematica

terms = 22;
CoefficientList[E^Total[x^Range[7]] + O[x]^terms, x] Range[0, terms-1]! (* Jean-François Alcover, Nov 11 2020 *)

Maxima

a(n):=if n=0 then 1 else n!*sum(sum((-1)^i*binomial(k, k-i)*binomial(n-7*i-1, k-1), i, 0, (n-k)/7)/k!, k, 1, n);
makelist(a(n),n,0,20);

Formula

E.g.f.: exp(Sum_{j=1..7} x^j).

a(n) = n!*sum(k=1..n, sum(i=0..(n-k)/7, (-1)^i*binomial(k,k-i)*binomial(n-7*i-1,k-1))/k!), n>0, a(0)=1.