cp's OEIS Frontend

A177826 Sub-triangle of A060187: even-indexed entries of even-indexed rows.

%I A177826 #16 Jun 25 2025 04:06:14
%S A177826 1,1,1,1,230,1,1,10543,10543,1,1,331612,4675014,331612,1,1,9116141,
%T A177826 906923282,906923282,9116141,1,1,237231970,121383780207,743288515164,
%U A177826 121383780207,237231970,1,1,6031771195,13342139253321,342917527152507,342917527152507,13342139253321,6031771195,1
%N A177826 Sub-triangle of A060187: even-indexed entries of even-indexed rows.
%e A177826 Triangle begins:
%e A177826   {1},
%e A177826   {1, 1},
%e A177826   {1, 230, 1},
%e A177826   {1, 10543, 10543, 1},
%e A177826   {1, 331612, 4675014, 331612, 1},
%e A177826   {1, 9116141, 906923282, 906923282, 9116141, 1},
%t A177826 p[x_, n_] = (1 - x)^(n + 1)*Sum[((2*k + 1)^n)*x^k, {k, 0, Infinity}];
%t A177826 t[n_, m_] := CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x][[m + 1]];
%t A177826 Table[Table[t[n, 2*m], {m, 0, Floor[n/2]}], {n, 0, 20, 2}];
%t A177826 Flatten[%]
%t A177826 (* Alternative recursion for A060187 *)
%t A177826 m = 2;
%t A177826 A[n_, 1] := 1
%t A177826 A[n_, n_] := 1
%t A177826 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 A177826 Table[A[n,k],{n,1,10,2},{k,1,n,2}]
%t A177826 (* Alternative expansion for A060187 *)
%t A177826 p[t_] = Exp[t] *x/(-Exp[2*t] + x)
%t A177826 Table[ CoefficientList[FullSimplify[ExpandAll[(n!*(-1 + x)^(n + \
%t A177826 1)/x)*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]]], x], {n, 0, 10}]
%Y A177826 Cf. A060187
%K A177826 nonn,tabl
%O A177826 0,5
%A A177826 _Roger L. Bagula_, Dec 13 2010