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A306026 Antidiagonal sums of A306024. 3
1, 1, 2, 5, 16, 66, 343, 2180, 16505, 145773, 1477880, 16986349, 219158316, 3147962668, 49982588535, 871766923048, 16609804758449, 344016348602845, 7711752589539436, 186379711851775401, 4839449174872615116, 134575228738532130948, 3996183953610068510929 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

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).

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);

CROSSREFS

Cf. A306024, A305971.

Sequence in context: A000522 A182290 A007469 * A091139 A084785 A124551

Adjacent sequences:  A306023 A306024 A306025 * A306027 A306028 A306029

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 17 2018

STATUS

approved

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Last modified March 23 14:17 EDT 2019. Contains 321431 sequences. (Running on oeis4.)