A344640 Antidiagonal sums of A344639.
1, 2, 5, 16, 63, 297, 1649, 10641, 78823, 662315, 6241889, 65294039, 751035233, 9420926879, 127958645921, 1870319380463, 29263787708393, 487891616911031, 8632986776222945, 161555987833199807, 3187606376603319017, 66128414623822131863, 1438861202348688524897, 32763278185929878499887
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..448
Programs
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Mathematica
Table[Sum[Sum[Abs[StirlingS1[n-k,m]](m+1)^k,{m,0,n-k}],{k,0,n}],{n,0,23}]
Formula
a(n) = Sum_{k=0..n} Sum_{m=0..n-k} abs(S1(n-k, m))*(m + 1)^k, where S1 indicates the signed Stirling numbers of first kind.
Conjecture: a(n) ~ n!. - Vaclav Kotesovec, May 26 2021