A131014 Sum of all n-digit Stirling numbers of first kind.

4, 61, 274, 1764, 13068, 109584, 1026576, 10628640, 120543840, 1486442880, 19802759040, 283465647360, 4339163001600, 70734282393600, 1223405590579200, 22376988058521600, 431565146817638400, 8752948036761600000, 186244810780170240000, 4148476779335454720000

Offset

1,1

Links

Table of n, a(n) for n=1..20.

Example

Sum of all 1-digit Stirling numbers is 0 + 1 + 3 = 4.
Sum of all 2-digit Stirling numbers is 11 + 50 = 61.
Sum of all 3-digit Stirling numbers is 274.

Mathematica

digNum[n_] := Length @ IntegerDigits[n]; stir[n_] := n! * HarmonicNumber[n]; digCount = 0; sum = 0; cumsum = {}; Do[s = stir[n]; If[digNum[s] > digCount, digCount++; AppendTo[cumsum, sum]]; sum += s, {n, 1, 25}]; Differences[cumsum] (* Amiram Eldar, Nov 30 2019 *)

Crossrefs

Cf. A000254.

Sequence in context: A071582 A158300 A129452 * A118005 A132064 A229666

Adjacent sequences: A131011 A131012 A131013 * A131015 A131016 A131017

Keyword

nonn,base,less

Author

Parthasarathy Nambi, Sep 24 2007

Extensions

More terms from Amiram Eldar, Nov 30 2019

Status

approved