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

1,1

Links

Table of n, a(n) for n=1..21.

Example

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.

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 *)

Crossrefs

Cf. A002736.

Sequence in context: A073066 A002736 A309318 * A059387 A126190 A121356

Adjacent sequences: A131969 A131970 A131971 * A131973 A131974 A131975

Keyword

nonn,base,less

Author

Parthasarathy Nambi, Oct 06 2007

Extensions

More terms from Amiram Eldar, Nov 30 2019

Status

approved