A392733 a(n) = Sum_{k=0..n} |Stirling1(n+k,k)|.

1, 1, 13, 281, 8691, 351625, 17612057, 1052705857, 73152856651, 5796006791037, 515777928208797, 50936751348311609, 5528394469691073475, 654111729553888537425, 83796907707907976374065, 11555724312003240036796545, 1706764715516969234087492715, 268812993066150470621848767445

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

a(n) ~ 2^(3*n) * w^(2*n+1) * n^(n - 1/2) / (sqrt(Pi*(w-1)) * exp(n) * (2*w-1)^(n+1)), where w = -LambertW(-1,-exp(-1/2)/2) = A202343 + 1/2 = 1.75643120862616967698...

Mathematica

Table[Sum[Abs[StirlingS1[n+k, k]], {k, 0, n}], {n, 0, 20}]

Crossrefs

Cf. A354980, A392734, A392744.

Cf. A202343.

Sequence in context: A133284 A012570 A256044 * A160294 A092145 A278628

Adjacent sequences: A392730 A392731 A392732 * A392734 A392735 A392736

Keyword

nonn

Author

Vaclav Kotesovec, Jan 21 2026

Status

approved