A162747 A factorial-Pascal matrix.

1, 1, 1, 1, 3, 1, 1, 6, 6, 1, 1, 10, 20, 10, 1, 1, 15, 50, 50, 15, 1, 1, 21, 105, 176, 105, 21, 1, 1, 28, 196, 497, 497, 196, 28, 1, 1, 36, 336, 1204, 1830, 1204, 336, 36, 1, 1, 45, 540, 2604, 5634, 5634, 2604, 540, 45, 1, 1, 55, 825, 5160, 15150, 21642, 15150, 5160, 825

Offset

0,5

Comments

Row sums are A162748.

Links

Table of n, a(n) for n=0..63.

Formula

Number triangle T(n,k)=sum{j=0..n, C(n,j)*C(n-j,2(k-j))*if(j<=k,(k-j)!,0)}.

G.f.: 1/(1-x-xy-x^2*y/(1-x-xy-x^2*y/(1-x-xy-2x^2*y/(1-x-xy-2x^2*y/(1-x-xy-3x^2*y/(1-... (continued fraction). [From Paul Barry, Apr 12 2010]

Example

Triangle begins
1,
1, 1,
1, 3, 1,
1, 6, 6, 1,
1, 10, 20, 10, 1,
1, 15, 50, 50, 15, 1,
1, 21, 105, 176, 105, 21, 1,
1, 28, 196, 497, 497, 196, 28, 1,
1, 36, 336, 1204, 1830, 1204, 336, 36, 1,
1, 45, 540, 2604, 5634, 5634, 2604, 540, 45, 1,
1, 55, 825, 5160, 15150, 21642, 15150, 5160, 825, 55, 1

Crossrefs

Sequence in context: A056241 A162745 A001263 * A107105 A088925 A100862

Adjacent sequences: A162744 A162745 A162746 * A162748 A162749 A162750

Keyword

easy,nonn,tabl

Author

Paul Barry, Jul 12 2009

Status

approved