A306026 Antidiagonal sums of A306024.

1, 1, 2, 5, 16, 66, 343, 2180, 16505, 145773, 1477880, 16986349, 219158316, 3147962668, 49982588535, 871766923048, 16609804758449, 344016348602845, 7711752589539436, 186379711851775401, 4839449174872615116, 134575228738532130948, 3996183953610068510929

Offset: 0

Author

Alois P. Heinz, Jun 17 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A306024, A305971.

Programs

Maple

b:= proc(n, k, m) option remember; `if`(n=0, 1,
      add(b(n-1, k, max(m, j)), j=1..m+k))
    end:
a:= n-> add(b(j, n-j, 0), j=0..n):
seq(a(n), n=0..25);
# second Maple program:
b:= (n, k)-> n!*coeff(series(exp(add((exp(j*x)-1)/j, j=1..k)), x, n+1), x, n):
a:= n-> add(b(j, n-j), j=0..n):
seq(a(n), n=0..25);

Formula

a(n) = Sum_{j=0..n} j! * [x^j] exp(Sum_{i=1..n-j} (exp(i*x)-1)/i).

a(n) = Sum_{j=0..n} A306024(j,n-j).