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 A123576 #12 Mar 29 2020 17:15:55
%S A123576 0,0,0,0,0,1,1,1,1,2,2,2,3,3,4,6,6,6,6,7,7,7,8,8,9,11,11,11,12,12,13,
%T A123576 15,15,16,18,21,21,21,21,22,22,22,23,23,24,26,26,26,27,27,28,30,30,31,
%U A123576 33,36,36,36,37,37,38,40,40,41,43,46,46,47,49,52,56,56,56,56,57,57,57,58
%N A123576 The Kruskal-Macaulay function L_4(n).
%C A123576 Write n (uniquely) as n = C(n_t,t) + C(n_{t-1},t-1) + ... + C(n_v,v) where n_t > n_{t-1} > ... > n_v >= v >= 1. Then L_t(n) = C(n_t,t+1) + C(n_{t-1},t) + ... + C(n_v,v+1).
%D A123576 D. E. Knuth, The Art of Computer Programming, Vol. 4, Fascicle 3, Section 7.2.1.3, Table 3.
%p A123576 lowpol := proc(n,t) local x::integer ; x := floor( (n*factorial(t))^(1/t)) ; while binomial(x,t) <= n do x := x+1 ; od ; RETURN(x-1) ; end: C := proc(n,t) local nresid,tresid,m,a ; nresid := n ; tresid := t ; a := [] ; while nresid > 0 do m := lowpol(nresid,tresid) ; a := [op(a),m] ; nresid := nresid - binomial(m,tresid) ; tresid := tresid-1 ; od ; RETURN(a) ; end: L := proc(n,t) local a ; a := C(n,t) ; add( binomial(op(i,a),t+2-i),i=1..nops(a)) ; end: A123576 := proc(n) L(n,4) ; end: for n from 0 to 80 do printf("%d, ",A123576(n)) ; od ; # _R. J. Mathar_, May 18 2007
%t A123576 (+ The function L(n,t) is defined in A123575 *)
%t A123576 a[n_] := L[n, 4];
%t A123576 a /@ Range[0, 80] (* _Jean-François Alcover_, Mar 29 2020 *)
%Y A123576 For L_i(n), i=1, 2, 3, 4, 5 see A000217, A111138, A123575, A123576, A123577.
%K A123576 nonn,easy
%O A123576 0,10
%A A123576 _N. J. A. Sloane_, Nov 12 2006
%E A123576 More terms from _R. J. Mathar_, May 18 2007