|
Search: id:A028338
|
|
|
| A028338 |
|
Triangle of coefficients in expansion of (x+1)(x+3)...(x+2n-1). |
|
+0
8
|
|
| 1, 1, 1, 3, 4, 1, 15, 23, 9, 1, 105, 176, 86, 16, 1, 945, 1689, 950, 230, 25, 1, 10395, 19524, 12139, 3480, 505, 36, 1, 135135, 264207, 177331, 57379, 10045, 973, 49, 1, 2027025, 4098240, 2924172, 1038016, 208054, 24640, 1708, 64, 1, 34459425
(list; table; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
LINKS
|
T. D. Noe, Rows n=0..50 of triangle, flattened
|
|
FORMULA
|
Triangle T(n, k), read by rows, given by [1, 2, 3, 4, 5, 6, 7, ...] DELTA [1, 0, 1, 0, 1, 0, 1, 0, ...] where DELTA is the operator defined in A084938 . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Feb 20 2005
T(n, k) = sum[(-2)^(n-i) binomial(i, k) s(n, i), i=k..n] where s(n, k) are signed Stirling numbers of the first kind. - Francis Woodhouse (fwoodhouse(AT)gmail.com), Nov 18 2005
|
|
EXAMPLE
|
E.g. For n=4, (x + 1) (x + 3) (x + 5) (x + 7) = x^4+16*x^3+86*x^2+176*x+105
1; 1,1; 3,4,1; 15,23,9,1; 105,176,86,16,1; ...
|
|
MATHEMATICA
|
T[n_, k_] := Sum[(-2)^(n-i) Binomial[i, k] StirlingS1[n, i], {i, k, n}] (Woodhouse)
|
|
CROSSREFS
|
A039757 is signed version.
Diagonals : A001147, A004041, A028339, A028340, A028341; A000012, A000290, A024196, A024197, A024198. Row sums : A000165
Adjacent sequences: A028335 A028336 A028337 this_sequence A028339 A028340 A028341
Sequence in context: A114189 A059110 A100326 this_sequence A039757 A136228 A055133
|
|
KEYWORD
|
tabl,nonn,easy,nice
|
|
AUTHOR
|
R. W. Gosper
|
|
|
Search completed in 0.002 seconds
|
