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

0,5

Comments

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.

Links

Table of n, a(n) for n=0..54.

Formula

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}.

Example

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.

Crossrefs

Cf. A080248, A008277.

Sequence in context: A111577 A176242 A036969 * A333143 A157154 A022168

Adjacent sequences: A080246 A080247 A080248 * A080250 A080251 A080252

Keyword

easy,nonn,tabl

Author

Paul Barry, Feb 17 2003

Status

approved