A374891 Obverse convolution (1)**A000984; see Comments.

2, 6, 42, 882, 62622, 15843366, 14655113550, 50311004817150, 647552943001537650, 31484671641677762080650, 5817013478501458288734652050, 4103513269179719224996951799587650, 11096544131445222000310082187517540861050

Offset: 0

Author

Clark Kimberling, Jul 31 2024

Keywords

• nonn

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences. This is a divisibility sequence (see Formula).

Crossrefs

Cf. A000012, A000984, A007685, A374848.

Programs

Mathematica

s[n_] := 1; t[n_] := Binomial[2 n, n];
u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
Table[u[n], {n, 0, 20}]

Formula

a(n+1) = a(n)*A244174(n+1) for n>=0 (conjectured) = a(n)*A323230(n+2) for n>=0 (conjectured).

a(n) ~ c * A007685(n), where c = Product_{k=0..oo} (1 + 1/binomial(2*k,k)) = 3.74782908533723753117687910314018231428739915473496578523053032212205053... - Vaclav Kotesovec, Jul 31 2024