|
| |
|
|
A156308
|
|
Inverse of triangle defined by sequence A156290
|
|
2
| |
|
|
1, 4, 1, 9, 6, 1, 16, 20, 8, 1, 25, 50, 35, 10, 1, 36, 105, 112, 54, 12, 1, 49, 196, 294, 210, 77, 14, 1, 64, 336, 672, 660, 352, 104, 16, 1, 81, 540, 1386, 1782, 1287, 546, 135, 18, 1, 100, 825, 2640, 4290, 4004, 2275, 800, 170, 20, 1
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| From Wolfdieter Lang, Jun 26 2011: (Start)
This triangle S(n,m) appears as U_m(n) in the Knuth reference on p. 285. It is related to the Riordan triangle A111125(n,m), appearing in this reference as T_m(n) on p. 285, by
S(n,m) = A111125(n,m) - A111125(n-1,m), n>=m>=1 (identity on p. 286).
Also, S(n,m)-S(n-1,m) = A111125(n-1,m-1), n>=2, m>=1 (identity on p. 286).
(End)
|
|
|
LINKS
| D. E. Knuth, Johann Faulhaber and sums of powers, Math. Comp. 61 (1993), no. 203, 277-294.
|
|
|
FORMULA
| S(n,m) = n/m * C(n + m - 1, 2*m - 1)
|
|
|
EXAMPLE
| S(3,1)=9, S(3,3)=1, S(5,3)=35
|
|
|
MATHEMATICA
| S[m_] := Flatten[Table[k/j Binomial[k + j - 1, 2 j - 1], {k, 1, m}, {j, 1, k}]]
|
|
|
CROSSREFS
| Column 1 of triangle is A000290
Column 2 of triangle is A002415
Column 3 of triangle is A040977
Column 4 of triangle is A053347
Column 5 of triangle is A054334
Sequence in context: A197258 A185780 A051672 * A092162 A073056 A049762
Adjacent sequences: A156305 A156306 A156307 * A156309 A156310 A156311
|
|
|
KEYWORD
| easy,nonn,tabl
|
|
|
AUTHOR
| Hartmut F. W. Hoeft (hhoft(AT)emich.edu), Feb 07 2009
|
| |
|
|
