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A177826
Sub-triangle of A060187: even-indexed entries of even-indexed rows.
0
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,...}.
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
Sequence in context: A178673 A028452 A072020 * A122269 A171666 A321503
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Dec 13 2010
STATUS
approved