This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A115082 #13 Sep 11 2024 12:22:28
%S A115082 1,2,5,20,94,507,3009,19350,132920,966962,7396366,59173897,492995320,
%T A115082 4262193275,38125138575,351960913470,3346157796060,32700768584100,
%U A115082 327957494280000,3370522049859990,35451669429671520,381183654441916290
%N A115082 Column 1 of triangle A115080.
%F A115082 From _Paul D. Hanna_, Feb 18 2007: (Start)
%F A115082 a(n) = A115081(n) + n*A115081(n-1).
%F A115082 a(n) = Sum_{k=0..[(n+1)/2]} A000108(n-k)*A000108(k)*(k+1)!*C(n+1,2*k)/2^k, where A000108(n) = C(2*n,n)/(n+1) is the n-th Catalan number. (End)
%o A115082 (PARI) {a(n)=sum(k=0,(n+1)\2,binomial(2*n-2*k,n-k)/(n-k+1)*binomial(2*k,k)/(k+1) *(k+1)!*binomial(n+1,2*k)/2^k)} \\ _Paul D. Hanna_, Feb 18 2007
%Y A115082 Cf. A115080, A115081 (column 0), A115083 (column 2), A115084 (row sums); A115087.
%Y A115082 Cf. A000108.
%K A115082 nonn
%O A115082 0,2
%A A115082 _Paul D. Hanna_, Jan 13 2006