A016225 -id:A016225 - cp's OEIS frontend

A080249 Stirling-like number triangle defined by the sequence A000292=C(n+3,3).

1, 1, 1, 1, 5, 1, 1, 21, 15, 1, 1, 85, 171, 35, 1, 1, 341, 1795, 871, 70, 1, 1, 1365, 18291, 19215, 3321, 126, 1, 1, 5461, 184275, 402591, 135450, 10377, 210, 1, 1, 21845, 1848211, 8236095, 5143341, 716562, 28017, 330, 1, 1, 87381, 18503955, 166570111, 188253030, 45270813, 3069990, 67617, 495, 1

Offset: 0

Paul Barry, Feb 17 2003

Columns include A002450, A016225. The defining sequence A000292=C(n+3,3) is the sequence of partial sums of the defining sequence for number triangle A080248.

			Triangle begins:
1;
1,    1;
1,    5,      1;
1,   21,     15,      1;
1,   85,    171,     35,      1;
1,  341,   1795,    871,     70,     1;
1, 1365,  18291,  19215,   3321,   126,   1;
1, 5461, 184275, 402591, 135450, 10377, 210, 1;
For example, 171 = 21+10*15, 35 = 15+20*1.

Cf. A080248, A008277.

T(n,k) = T(n-1,k-1) + A000292(k)*T(n-1,k). Columns are generated by 1/product{k=0..n, 1-C(k+3,3)*x}.

A080250 Expansion of 1/((1-x)(1-4x)(1-10x)(1-20x)).

Original entry on oeis.org

1, 35, 871, 19215, 402591, 8236095, 166570111, 3349906175, 67183250431, 1345516627455, 26928850135551, 538762184167935, 10777095520297471, 215560428864815615, 4311393762242888191, 86229727095755178495

Offset: 0

Paul Barry, Feb 17 2003

Column k=3 in number triangle A080249.

Vincenzo Librandi, Table of n, a(n) for n = 0..300
Index entries for linear recurrences with constant coefficients, signature (35,-354,1120,-800).

Cf. A080249, A016225, A000292.

[(1350*20^n-950*10^n+114*4^n-1)/513: n in [0..20]]; // Vincenzo Librandi, Aug 05 2013

CoefficientList[Series[1/((1-x)(1-4x)(1-10x)(1-20x)),{x,0,20}],x] (* or *) Table[(1350*20^n-950*10^n+114*4^n-1)/513,{n,0,20}] (* or *) LinearRecurrence[{35,-354,1120,-800},{1,35,871,19215},21] (* Harvey P. Dale, Apr 25 2011 *)

G.f.: 1/((1-x)*(1-4*x)*(1-10*x)*(1-20*x)).
a(n) = (1350*20^n-950*10^n+114*4^n-1)/513.
a(0)=1, a(1)=35, a(2)=871, a(3)=19215, a(n) = 35*a(n-1) -354*a(n-2) +1120*a(n-3) -800*a(n-4). - Harvey P. Dale, Apr 25 2011

Corrected by T. D. Noe, Nov 08 2006

cp's OEIS Frontend

A080249 Stirling-like number triangle defined by the sequence A000292=C(n+3,3).

Views

Author

Keywords

Comments

Examples

Crossrefs

Formula

A080250 Expansion of 1/((1-x)(1-4x)(1-10x)(1-20x)).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

Formula

Extensions