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%I #11 Nov 30 2019 09:12:40
%S 2,24,180,7420,33264,991848,3938220,103832872,389398464,9620555000,
%T 34901442000,828288777420,2940343837200,67898251759800,
%U 237371722628040,5373868753340880,97581248745060600,335240928272918304,7415892272293658608,25286571126114014640,553714770886681187168
%N Sum of all n-digit Apery numbers.
%e Sum of all 1-digit Apery numbers is 0 + 2 = 2.
%e Sum of all 2-digit Apery numbers is 24
%e Sum of all 3-digit Apery numbers is 180.
%t digNum[n_] := Length @ IntegerDigits[n]; apery[n_] := n^2 * Binomial[2n, n]; digCount = 0; sum = 0; cumsum = {}; Do[a = apery[n]; If[digNum[a] > digCount, digCount++; AppendTo[cumsum, sum]]; sum += a, {n, 0, 35}]; Differences[cumsum] (* _Amiram Eldar_, Nov 30 2019 *)
%Y Cf. A002736.
%K nonn,base,less
%O 1,1
%A _Parthasarathy Nambi_, Oct 06 2007
%E More terms from _Amiram Eldar_, Nov 30 2019