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%I #38 Sep 27 2023 03:58:57
%S 1,2,5,14,39,122,387,1328,4675,17414,66743,267234,1100453,4696414,
%T 20580433,92966560,430394961,2046068386,9950230149,49544789182,
%U 251930150903,1308655057210,6931418152099,37435337021328,205874622937315,1152718809407558,6564213262312871
%N Sum of coefficients in the expansion of Sum_{y a composition of n} p(y) in terms of Schur functions, where p is power-sum symmetric functions.
%C From _Hsin-Chieh Liao_, Mar 25 2021: (Start)
%C Sum of coefficients of the Schur expansion of sum of Eulerian quasisymmetric functions Q_n,d over d from 0 to n-1.
%C a(n) is the number of marked tableaux with cells filled with 1,2,...,n. In Stembridge's paper, he gave a refinement of this number by the shape and the index of the tableaux. (End)
%H Ludovic Schwob, <a href="/A317553/b317553.txt">Table of n, a(n) for n = 1..43</a>
%H Ludovic Schwob, <a href="/A317553/a317553.txt">Sage program</a>
%H John Shareshian and Michelle. L. Wachs, <a href="https://doi.org/10.1016/j.aim.2010.05.009">Eulerian quasisymmetric functions</a>, Advanced in Mathematics, 225(6) (2010), 2921-2966.
%H John R. Stembridge, <a href="https://doi.org/10.1016/0012-365X(92)90378-S">Eulerian numbers, tableaux, and the Betti numbers of a toric variety</a>, Discrete Mathematics, 99 (1992), 307-320.
%e We have p(4) + p(22) + 2 p(31) + 3 p(211) + p(1111) = 8 s(4) + 2 s(22) + 4 s(31), which has sum of coefficients a(4) = 14.
%o (Sage) # See Links - _Ludovic Schwob_, Sep 26 2023
%Y Cf. A000085, A082733, A153452, A296188, A296561, A300121, A304438, A317552, A317554.
%K nonn
%O 1,2
%A _Gus Wiseman_, Sep 14 2018
%E a(11) onwards from _Ludovic Schwob_, Sep 26 2023
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