A131972 Sum of all n-digit Apery numbers.

2, 24, 180, 7420, 33264, 991848, 3938220, 103832872, 389398464, 9620555000, 34901442000, 828288777420, 2940343837200, 67898251759800, 237371722628040, 5373868753340880, 97581248745060600, 335240928272918304, 7415892272293658608, 25286571126114014640, 553714770886681187168

Offset: 1

Author

Parthasarathy Nambi, Oct 06 2007

Keywords

• nonn
• base
• less

Examples

			Sum of all 1-digit Apery numbers is 0 + 2 = 2.
Sum of all 2-digit Apery numbers is 24
Sum of all 3-digit Apery numbers is 180.
		

Crossrefs

Cf. A002736.

Programs

Mathematica

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 *)

Extensions

More terms from Amiram Eldar, Nov 30 2019