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Coefficients in expansion of Pi as Sum_{n>=1} a(n)/(n*n!*(n+1)!), as found by greedy algorithm.
2

%I #14 Mar 11 2022 04:52:35

%S 6,3,7,4,18,1,21,35,76,82,56,25,98,149,111,170,166,195,113,306,221,

%T 367,533,373,360,675,7,262,194,669,776,1083,384,617,725,752,122,1131,

%U 514,992,1238,600,1380,1306,1991,1983,114,2021,534,1660,192,733,1596,1898

%N Coefficients in expansion of Pi as Sum_{n>=1} a(n)/(n*n!*(n+1)!), as found by greedy algorithm.

%t seq[cons_, len_] := Module[{s = {}, n = 0, c = cons, m}, While[n < len, n++; m = Floor[c*(n*n!*(n + 1)!)]; AppendTo[s, m]; c -= m/(n*n!*(n + 1)!)]; s]; seq[Pi, 50] (* _Amiram Eldar_, Mar 11 2022 *)

%Y Cf. A000796, A011189, A011193.

%K nonn

%O 1,1

%A _N. J. A. Sloane_.

%E Offset corrected and more terms from _Sean A. Irvine_, Jun 14 2018