A354980 a(n) = Sum_{k=0..n} |Stirling1(k + n, n)|, row sums of A354979.

1, 2, 15, 267, 7600, 293925, 14309743, 838738740, 57454922915, 4502651972249, 397234757906030, 38956074787666025, 4203685743662913937, 494961608467205567662, 63146302129222660054495, 8676907380290993545719955, 1277582548576381271300740092, 200667260023390039020841648045

Offset

0,2

Comments

In general, for m >= 1, Sum_{k=0..n} Stirling1(n + m*k,n) ~ (m+1)^((2*m+1)*n-1/2) * w^((m+1)*n) * n^(m*n - 1/2) / (sqrt(2*Pi*(w-1)) * exp(m*n) * ((m+1)*w - 1)^(m*n)), where w = -LambertW(-1,-exp(-1/(m+1))/(m+1)). - Vaclav Kotesovec, Jan 22 2026

Links

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

Formula

a(n) ~ 2^(3*n-1) * c^(2*n) * n^(n - 1/2) / (sqrt(Pi*(c-1)) * (2*c-1)^n * exp(n)), where c = -LambertW(-1,-exp(-1/2)/2) = 1.7564312086261696769827376166... - Vaclav Kotesovec, Jun 15 2022

Mathematica

Table[Sum[Abs@StirlingS1[k + n, n], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jun 15 2022 *)

Crossrefs

Cf. A354979, A132393, A392733.

Sequence in context: A264907 A195737 A192567 * A143886 A174482 A381983

Adjacent sequences: A354977 A354978 A354979 * A354981 A354982 A354983

Keyword

nonn

Author

Peter Luschny, Jun 15 2022

Status

approved