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, 1

Offset

0,5

Comments

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

686233400119951360, 838856713968361013248, 1275735509232452907827200,...}.

Links

Table of n, a(n) for n=0..36.

Example

{1},
{1, 1},
{1, 230, 1},
{1, 10543, 10543, 1},
{1, 331612, 4675014, 331612, 1},
{1, 9116141, 906923282, 906923282, 9116141, 1},

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, 10}, {k, n}]]
(* 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}]

Crossrefs

Cf. A060187

Sequence in context: A178673 A028452 A072020 * A122269 A171666 A321503

Adjacent sequences: A177823 A177824 A177825 * A177827 A177828 A177829

Keyword

nonn,tabl

Author

Roger L. Bagula, Dec 13 2010

Status

approved