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A156045 A triangle sequence made symmetrical by reverse coefficients: t0(n,m)=2 + n! - m! - (n - m)!; t(n,m)=(t0(n,m)+Reverse[t0(n,m)])/2 0
1, 1, 1, 1, 2, 1, 1, 5, 5, 1, 1, 19, 22, 19, 1, 1, 97, 114, 114, 97, 1, 1, 601, 696, 710, 696, 601, 1, 1, 4321, 4920, 5012, 5012, 4920, 4321, 1, 1, 35281, 39600, 40196, 40274, 40196, 39600, 35281, 1, 1, 322561, 357840, 362156, 362738, 362738, 362156, 357840 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{{1, 2, 4, 12, 62, 424, 3306, 28508, 270430, 2810592, 31840994},...}.

LINKS

Table of n, a(n) for n=0..52.

FORMULA

t0(n,m)=2 + n! - m! - (n - m)!;

t(n,m)=(t0(n,m)+Reverse[t0(n,m)])/2

EXAMPLE

{1},

{1, 1},

{1, 2, 1},

{1, 5, 5, 1},

{1, 19, 22, 19, 1},

{1, 97, 114, 114, 97, 1},

{1, 601, 696, 710, 696, 601, 1},

{1, 4321, 4920, 5012, 5012, 4920, 4321, 1},

{1, 35281, 39600, 40196, 40274, 40196, 39600, 35281, 1},

{1, 322561, 357840, 362156, 362738, 362738, 362156, 357840, 322561, 1},

{1, 3265921, 3588480, 3623756, 3628058, 3628562, 3628058, 3623756, 3588480, 3265921, 1

MATHEMATICA

Clear[t];

t[n_, m_] = 2 + n! - m! - (n - m)!;

Table[(Table[t[n, m], {m, 0, n}] + Reverse[Table[t[n, m], {m, 0, n}]])/2, {n, 0, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A211400 A060854 A091378 * A119687 A086856 A052916

Adjacent sequences:  A156042 A156043 A156044 * A156046 A156047 A156048

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 02 2009

STATUS

approved

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Last modified February 24 03:21 EST 2018. Contains 299595 sequences. (Running on oeis4.)