Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #7 Aug 02 2024 18:59:44
%S 2,6,42,882,62622,15843366,14655113550,50311004817150,
%T 647552943001537650,31484671641677762080650,
%U 5817013478501458288734652050,4103513269179719224996951799587650,11096544131445222000310082187517540861050
%N Obverse convolution (1)**A000984; see Comments.
%C See A374848 for the definition of obverse convolution and a guide to related sequences. This is a divisibility sequence (see Formula).
%F a(n+1) = a(n)*A244174(n+1) for n>=0 (conjectured) = a(n)*A323230(n+2) for n>=0 (conjectured).
%F a(n) ~ c * A007685(n), where c = Product_{k=0..oo} (1 + 1/binomial(2*k,k)) = 3.74782908533723753117687910314018231428739915473496578523053032212205053... - _Vaclav Kotesovec_, Jul 31 2024
%t s[n_] := 1; t[n_] := Binomial[2 n, n];
%t u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
%t Table[u[n], {n, 0, 20}]
%Y Cf. A000012, A000984, A007685, A374848.
%K nonn
%O 0,1
%A _Clark Kimberling_, Jul 31 2024