A167172 Triangle T(n,k) read by rows: 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

Offset

0,5

Comments

Row sums are: {1, 2, 4, 8, 17, 34, 71, 140, 291, 570, 1201,...}.

Links

G. C. Greubel, Table of n, a(n) for the first 50 rows

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

Cf. A140356.

Sequence in context: A022818 A050447 A248601 * A173075 A166293 A094525

Adjacent sequences: A167169 A167170 A167171 * A167173 A167174 A167175

Keyword

nonn,tabl

Author

Roger L. Bagula, Oct 29 2009

Extensions

Edited by the OEIS editors, Jun 05 2016

Status

approved