A177826 - OEIS

%I #8 Mar 12 2014 16:37:17

%S 1,1,1,1,230,1,1,10543,10543,1,1,331612,4675014,331612,1,1,9116141,

%T 906923282,906923282,9116141,1,1,237231970,121383780207,743288515164,

%U 121383780207,237231970,1,1,6031771195,13342139253321,342917527152507,342917527152507,13342139253321,6031771195,1,1

%N Sub-triangle of A060187: even-indexed entries of even-indexed rows.

%C Row sums are:{1, 2, 232, 21088, 5338240, 1832078848, 986530539520, 712531396354048,

%C 686233400119951360, 838856713968361013248, 1275735509232452907827200,...}.

%e {1},

%e {1, 1},

%e {1, 230, 1},

%e {1, 10543, 10543, 1},

%e {1, 331612, 4675014, 331612, 1},

%e {1, 9116141, 906923282, 906923282, 9116141, 1},

%t p[x_, n_] = (1 - x)^(n + 1)*Sum[((2*k + 1)^n)*x^k, {k, 0, Infinity}];

%t t[n_, m_] := CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x][[m + 1]];

%t Table[Table[t[n, 2*m], {m, 0, Floor[n/2]}], {n, 0, 20, 2}];

%t Flatten[%]

%t (*Alternative recursion for A060187*)

%t m = 2;

%t A[n_, 1] := 1

%t A[n_, n_] := 1

%t A[n_, k_] := A[n, k] = (m*n - m*k + 1)A[n - 1, k - 1] + (m*k - (m - 1))A[n - 1, k]

%t Table[A[n,k],{n,10},{k,n}]]

%t (* Alternative expansion for A060187*)

%t p[t_] = Exp[t] *x/(-Exp[2*t] + x)

%t Table[ CoefficientList[FullSimplify[ExpandAll[(n!*(-1 + x)^(n + \

%t 1)/x)*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]]], x], {n, 0, 10}]

%Y Cf. A060187

%K nonn,tabl

%O 0,5

%A _Roger L. Bagula_, Dec 13 2010