STATUS
proposed
approved
The OEIS is supported by the many generous donors to the OEIS Foundation.
proposed
approved
editing
proposed
A symmetrical triangular sequenceTriangle T(n,k) read by rows: t[T(n,k] ) = Binomial[binomial(n, k] ) + A140356[(n, k] ) - 1.
t[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.
nonn,uned,tabl,changed
Edited by the OEIS editors, Jun 05 2016
reviewed
editing
proposed
reviewed
editing
proposed
t[n,k] = Binomial[binomial(n, k] ) + A140356[(n, k] ) - 1 = Binomial[binomial(n, k] ) + If[if(k less than equal Floor[floor(n/2], ), Gamma[(k + 1], ), Gamma[(n - k + 1]] )) - 1.
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}]]
Flatten[Table[Table[t[n, k], {k, 0, n}], {n, 0, 10}]]
proposed
editing
editing
proposed
A symmetrical triangular sequence: t[n,k] = Binomial[n, k] + A140356[n, k] - 1.
Row sums are: {1, 2, 4, 8, 17, 34, 71, 140, 291, 570, 1201,...}.
{1, 2, 4, 8, 17, 34, 71, 140, 291, 570, 1201,...}
G. C. Greubel, <a href="/A167172/b167172.txt">Table of n, a(n) for the first 50 rows</a>
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.
=Binomial[n, k] + If[k less than equal Floor[n/2], Gamma[k + 1], Gamma[n - k + 1]] - 1
{1, 10, 46, 125, 233, 371, 233, 125, 46, 10, 1}.
t[n_, k_] = Binomial[n, k] + If[k <= Floor[n/2], Gamma[k + 1], Gamma[n - k + 1]] - 1;
Cf. A140356.
approved
editing
_Roger L. Bagula (rlbagulatftn(AT)yahoo.com), _, Oct 29 2009
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
0,5
Row sums are:
{1, 2, 4, 8, 17, 34, 71, 140, 291, 570, 1201,...}
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
{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
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}]]
nonn,uned
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Oct 29 2009
approved