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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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified May 30 18:38 EDT 2020. Contains 334728 sequences. (Running on oeis4.)