A156593 - OEIS

%I #7 Apr 06 2022 07:45:13

%S 1,1,1,1,-2,1,1,2,2,1,1,2,-2,2,1,1,-6,6,6,-6,1,1,-14,-42,-42,-42,-14,

%T 1,1,26,182,-546,-546,182,26,1,1,178,-2314,16198,-48594,16198,-2314,

%U 178,1,1,90,-8010,-104130,728910,728910,-104130,-8010,90,1,1,-2382,107190

%N Triangle: q=2; m=1; t(n,k) = If[m == 0, n!, Product[Sum[(-1)^i*StirlingS2[ k - 1, i]*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]; b(n,k,m) = If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])].

%e {1},

%e {1, 1},

%e {1, -2, 1},

%e {1, 2, 2, 1},

%e {1, 2, -2, 2, 1},

%e {1, -6, 6, 6, -6, 1},

%e {1, -14, -42, -42, -42, -14, 1},

%e {1, 26, 182, -546, -546, 182, 26, 1},

%e {1, 178, -2314, 16198, -48594, 16198, -2314, 178, 1},

%e {1, 90, -8010, -104130, 728910, 728910, -104130, -8010, 90, 1},

%e {1, -2382, 107190, 9539910, 124018830, 289377270, 124018830, 9539910, 107190, -2382, 1}

%t t[n_, m_] = If[m == 0, n!, Product[Sum[(-1)^i* StirlingS2[k - 1, i]*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]];

%t b[n_, k_, m_] = f[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])];

%t Table[Flatten[Table[Table[b[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 15}]

%K sign,tabl,uned

%O 0,5

%A _Roger L. Bagula_, Feb 10 2009