A173312 Partial sums of A005130.

1, 2, 4, 11, 53, 482, 7918, 226266, 11076482, 922911942, 130457184642, 31226202037017, 12642538061714517, 8652026056359367017, 10004193381504526849017, 19539080428042781631746217

Offset

0,2

Comments

Partial sums of Robbins numbers. Partial sums of the number of descending plane partitions whose parts do not exceed n. Partial sums of the number of n X n alternating sign matrices (ASM's). After 2, 11, 53, when is this partial sum again prime, as it is not again prime through a(32)?

Links

Table of n, a(n) for n=0..15.

Formula

a(n) = Sum_{i=0..n} A005130(i) = Sum_{i=0..n} Product_{k=0..i-1} (3k+1)!/(i+k)!. [corrected by Vaclav Kotesovec, Oct 26 2017]

a(n) ~ Pi^(1/3) * exp(1/36) * 3^(3*n^2/2 - 7/36) / (A^(1/3) * Gamma(1/3)^(2/3) * n^(5/36) * 2^(2*n^2 - 5/12)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Oct 26 2017

Example

a(17) = 1 + 1 + 2 + 7 + 42 + 429 + 7436 + 218348 + 10850216 + 911835460 + 129534272700 + 31095744852375 + 12611311859677500 + 8639383518297652500 + 9995541355448167482000 + 19529076234661277104897200 + 64427185703425689356896743840 + 358869201916137601447486156417296.

Mathematica

Table[Sum[Product[(3 k + 1)!/(j + k)!, {k, 0, j - 1}], {j, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 26 2017 *)
Accumulate[Table[Product[(3k+1)!/(n+k)!, {k, 0, n-1}], {n, 0, 20}]] (* Harvey P. Dale, Feb 06 2019 *)

Crossrefs

Cf. A005130, A006366, A048601, also A003827, A005156, A005158, A005160-A005164, A050204, A049503, A160707, A160708.

Sequence in context: A057857 A352969 A091233 * A351184 A156434 A007903

Adjacent sequences: A173309 A173310 A173311 * A173313 A173314 A173315

Keyword

nonn

Author

Jonathan Vos Post, Feb 16 2010

Status

approved