A160708 -id:A160708 - cp's OEIS frontend

A160707 Convolution square root of the Robbins sequence, A005130, starting with offset 1.

1, 1, 3, 18, 192, 3472, 104964, 5306272, 450215638, 64298445920

Offset: 1

Gary W. Adamson, May 24 2009

Terms are not integral beyond what's shown! - Joerg Arndt, Jan 02 2019

			Self-convolution = the Robbins sequence, A005130: (1, 2, 7, 42, 429, 7436, ...).
Example: A005130(4) = 42 = (1, 1, 3, 18) dot (18, 3, 1, 1) = (18 + 3 + 3 + 18).
The reversed procedure given (1, 2, 7, 42, ...) for a(4) = 18 = (1/2) * (42 - 2*a(3)) = (1/2) * 36 = 18.

Cf. A005130, A160708.

A173312 Partial sums of A005130.

Original entry on oeis.org

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

Offset: 0

Jonathan Vos Post, Feb 16 2010

nonn

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)?

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

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

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 *)

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

cp's OEIS Frontend

A160707 Convolution square root of the Robbins sequence, A005130, starting with offset 1.

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