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

1, 1, 1, 1, 230, 1, 1, 10543, 10543, 1, 1, 331612, 4675014, 331612, 1, 1, 9116141, 906923282, 906923282, 9116141, 1, 1, 237231970, 121383780207, 743288515164, 121383780207, 237231970, 1, 1, 6031771195, 13342139253321, 342917527152507, 342917527152507, 13342139253321, 6031771195, 1

Offset: 0

Author

Roger L. Bagula, Dec 13 2010

Keywords

• nonn
• tabl

Examples

			Triangle begins:
  {1},
  {1, 1},
  {1, 230, 1},
  {1, 10543, 10543, 1},
  {1, 331612, 4675014, 331612, 1},
  {1, 9116141, 906923282, 906923282, 9116141, 1},
		

Crossrefs

Cf. A060187

Programs

Mathematica

p[x_, n_] = (1 - x)^(n + 1)*Sum[((2*k + 1)^n)*x^k, {k, 0, Infinity}];
t[n_, m_] := CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x][[m + 1]];
Table[Table[t[n, 2*m], {m, 0, Floor[n/2]}], {n, 0, 20, 2}];
Flatten[%]
(* Alternative recursion for A060187 *)
m = 2;
A[n_, 1] := 1
A[n_, n_] := 1
A[n_, k_] := A[n, k] = (m*n - m*k + 1)A[n - 1, k - 1] + (m*k - (m - 1))A[n - 1, k]
Table[A[n,k],{n,1,10,2},{k,1,n,2}]
(* Alternative expansion for A060187 *)
p[t_] = Exp[t] *x/(-Exp[2*t] + x)
Table[ CoefficientList[FullSimplify[ExpandAll[(n!*(-1 + x)^(n + \
1)/x)*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]]], x], {n, 0, 10}]