The On-Line Encyclopedia of Integer Sequences (OEIS)

A167172 revision #2

A167172

A symmetrical triangular sequence:t[n,k]=Binomial[n, k] + A140356[n, k] - 1

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 7, 4, 1, 1, 5, 11, 11, 5, 1, 1, 6, 16, 25, 16, 6, 1, 1, 7, 22, 40, 40, 22, 7, 1, 1, 8, 29, 61, 93, 61, 29, 8, 1, 1, 9, 37, 89, 149, 149, 89, 37, 9, 1, 1, 10, 46, 125, 233, 371, 233, 125, 46, 10, 1

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

OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 4, 8, 17, 34, 71, 140, 291, 570, 1201,...}

LINKS

Table of n, a(n) for n=0..65.

FORMULA

t[n,k]=Binomial[n, k] + A140356[n, k] - 1

=Binomial[n, k] + If[k less than equal Floor[n/2], Gamma[k + 1], Gamma[n - k + 1]] - 1

EXAMPLE

{1},

{1, 1},

{1, 2, 1},

{1, 3, 3, 1},

{1, 4, 7, 4, 1},

{1, 5, 11, 11, 5, 1},

{1, 6, 16, 25, 16, 6, 1},

{1, 7, 22, 40, 40, 22, 7, 1},

{1, 8, 29, 61, 93, 61, 29, 8, 1},

{1, 9, 37, 89, 149, 149, 89, 37, 9, 1},

{1, 10, 46, 125, 233, 371, 233, 125, 46, 10, 1

MATHEMATICA

t[n_, k_] = Binomial[n, k] + If[k <= Floor[n/2], Gamma[k + 1], Gamma[n - k + 1]] - 1

Flatten[Table[Table[t[n, k], {k, 0, n}], {n, 0, 10}]]

CROSSREFS

A140356

Sequence in context: A022818 A050447 A248601 * A173075 A166293 A094525

Adjacent sequences: A167169 A167170 A167171 * A167173 A167174 A167175

KEYWORD

nonn,uned,changed

AUTHOR

Roger L. Bagula, Oct 29 2009

STATUS

approved