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 A349737 #19 Dec 01 2021 20:23:20
%S A349737 14,1001,326876,463991880,2789279908316,69923143311577493,
%T A349737 7237577480931700810180,3072423560706808979836029648,
%U A349737 5323553660882471719158839565113262,37516291344074264662783594047461175379710,124094883176124104767115229835643366860919133861769398480
%N A349737 a(n) is the common difference of the increasing arithmetic progression C(m,k), C(m,k+1), C(m,k+2) when C(m,k) = A349736(n).
%C A349737 For further information, see A349736.
%F A349737 a(n) = (2/n) * binomial(n^2+4n+2,(n^2+3n-2)/2) = (2/n) * A349476(n) for n >= 1.
%F A349737 a(n) ~ c*2^(n^2+4*n)/n^2, where c = 8*sqrt(2/(Pi*e)). - _Stefano Spezia_, Nov 29 2021
%e A349737 For n = 1, row 7 of Pascal's triangle is 1, 7, 21, 35, 35, 21, 7, 1; C(7,1) = 7, C(7,2) = 21 and C(7,3) = 35 form an arithmetic progression with common difference = 14, hence a(3) = 14.
%e A349737 For n = 2, row 14 is 1, 14, 91, 364, 1001, 2002, 3003, 3432, 3003, 2002, 1001, 364, 91, 14, 1; C(14,4) = 1001 , C(14,5) = 2002 and C(14,6) = 3003 form an arithmetic progression with common difference = 1001, hence a(4) = 1001.
%p A349737 Sequence = seq((2/n)*binomial(n^2+4*n+2,(n^2+3*n-2)/2), n=1..16);
%t A349737 nterms=15; Table[2/n*Binomial[n^2+4n+2, (n^2+3n-2)/2], {n, nterms}] (* _Paolo Xausa_, Nov 29 2021 *)
%Y A349737 Cf. A007318, A349736.
%K A349737 nonn
%O A349737 1,1
%A A349737 _Bernard Schott_, Nov 28 2021