cp's OEIS Frontend

A137597 Triangle read by rows: A008277 * A007318.

%I A137597 #13 Aug 31 2023 10:54:36
%S A137597 1,2,1,5,5,1,15,22,9,1,52,99,61,14,1,203,471,385,135,20,1,877,2386,
%T A137597 2416,1140,260,27,1,4140,12867,15470,9156,2835,455,35,1,21147,73681,
%U A137597 102215,72590,28441,6230,742,44,1
%N A137597 Triangle read by rows: A008277 * A007318.
%C A137597 Row sums = A035009 starting (1, 3, 11, 47, 227, ...).
%H A137597 Michael De Vlieger, <a href="/A137597/b137597.txt">Table of n, a(n) for n = 1..11325</a> (rows n = 1..150, flattened)
%H A137597 Zhanar Berikkyzy, Pamela E. Harris, Anna Pun, Catherine Yan, and Chenchen Zhao, <a href="https://arxiv.org/abs/2308.14183">Combinatorial Identities for Vacillating Tableaux</a>, arXiv:2308.14183 [math.CO], 2023. See p. 16.
%F A137597 A008277 * A007318 as infinite lower triangular matrices.
%e A137597 First few rows of the triangle:
%e A137597     1;
%e A137597     2,   1;
%e A137597     5,   5,   1;
%e A137597    15,  22,   9,   1;
%e A137597    52,  99,  61,  14,  1;
%e A137597   203, 471, 385, 135, 20, 1;
%e A137597   ...
%p A137597 T:= (n, k)-> add(Stirling2(n, j)*binomial(j-1, k-1), j=k..n):
%p A137597 seq(seq(T(n, k), k=1..n), n=1..10);  # _Alois P. Heinz_, Sep 03 2019
%t A137597 Table[Sum[StirlingS2[n, j]*Binomial[j - 1, k - 1], {j, k, n}], {n, 9}, {k, n}] // Flatten (* _Michael De Vlieger_, Aug 31 2023 *)
%Y A137597 Cf. A035009, A008277.
%Y A137597 Cf. A126350.
%K A137597 nonn,tabl
%O A137597 1,2
%A A137597 _Gary W. Adamson_, Jan 29 2008