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A131014 Sum of all n-digit Stirling numbers of first kind. 0

%I

%S 4,61,274,1764,13068,109584,1026576,10628640,120543840,1486442880,

%T 19802759040,283465647360,4339163001600,70734282393600,

%U 1223405590579200,22376988058521600,431565146817638400,8752948036761600000,186244810780170240000,4148476779335454720000

%N Sum of all n-digit Stirling numbers of first kind.

%e Sum of all 1-digit Stirling numbers is 0 + 1 + 3 = 4.

%e Sum of all 2-digit Stirling numbers is 11 + 50 = 61.

%e Sum of all 3-digit Stirling numbers is 274.

%t 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 *)

%Y Cf. A000254.

%K nonn,base,less

%O 1,1

%A _Parthasarathy Nambi_, Sep 24 2007

%E More terms from _Amiram Eldar_, Nov 30 2019

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)