cp's OEIS Frontend

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.

A073148 Triangle of numbers {a(n,k), n >= 0, 0<=k<=n} defined by a(0,0)=1, a(n,0)=A006013(n), a(n+1,n)=A001764(n+1), a(n,m) = Sum A001764(n-k)*a(n,k), k=0..m.

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%I A073148 #9 Jul 15 2021 15:07:30
%S A073148 1,2,3,7,9,12,30,37,43,55,143,173,194,218,273,728,871,961,1045,1155,
%T A073148 1428,3876,4604,5033,5393,5778,6324,7752,21318,25194,27378,29094,
%U A073148 30744,32655,35511,43263,120175
%N A073148 Triangle of numbers {a(n,k), n >= 0, 0<=k<=n} defined by a(0,0)=1, a(n,0)=A006013(n), a(n+1,n)=A001764(n+1), a(n,m) = Sum A001764(n-k)*a(n,k), k=0..m.
%C A073148 Compare to A073147. Related to generalized Catalan numbers; in particular, C(3n,n)/(2n+1) (enumerates ternary trees and also non-crossing trees)(A001764).
%C A073148 These numbers are cardinalities of some intervals in the Tamari lattices. - _F. Chapoton_, Jul 15 2021
%F A073148 a(n, m) = Sum A001764(n-k)*a(n, k), k=0..m.
%e A073148 {1}, {2,3}, {7,9,12}, {30,37,43,55}, {143,173,194,218,273},{728,871,961,1045,1155,1428}, {3876,4604,5033,5393,5778,6324,7752}, ...
%Y A073148 Cf. A073147, A001764, A006013, A006629, A028364.
%K A073148 easy,nonn,tabl
%O A073148 0,2
%A A073148 _Paul D. Hanna_, Jul 18 2002