|
| |
|
|
A137375
|
|
Triangular sequence from coefficients of Mahler polynomials from expansion of: p(x)=Exp[x*(1 + t - Exp[t])] with weight n!:M(x,n).
|
|
0
| |
|
|
1, 0, 0, -1, 0, -1, 0, -1, 3, 0, -1, 10, 0, -1, 25, -15, 0, -1, 56, -105, 0, -1, 119, -490, 105, 0, -1, 246, -1918, 1260, 0, -1, 501, -6825, 9450, -945
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,9
|
|
|
COMMENTS
| Row sums are: A000587
M(n,x):=sum(k=0..n, (x)^k*sum(j=0..k, binomial(n,k-j)*stirling2(n-k+j,j)*(-1)^j)). [From Vladimir Kruchinin, Jan 13 2012]
|
|
|
REFERENCES
| Weisstein, Eric W., Mahler Polynomial. http://mathworld.wolfram.com/MahlerPolynomial.html
|
|
|
FORMULA
| p(x)=Exp[x*(1 + t - Exp[t])]-> M(x,n) out(n,m)Coefficients(n!M(x,n))
T(n,k):=sum(j=0..k, binomial(n,k-j)*stirling2(n-k+j,j)*(-1)^(j)). [From Vladimir Kruchinin, Jan 13 2012]
|
|
|
EXAMPLE
| {1},
{0},
{0, -1},
{0, -1},
{0, -1, 3},
{0, -1, 10},
{0, -1, 25, -15},
{0, -1, 56, -105},
{0, -1, 119, -490, 105},
{0, -1, 246, -1918, 1260},
{0, -1, 501, -6825, 9450, -945}
|
|
|
MATHEMATICA
| Clear[p, x, t] p[t_] = Exp[x*(1 + t - Exp[t])]; Table[ ExpandAll[n!*SeriesCoefficient[Series[p[t], {t, 0, 30}], n]], {n, 0, 10}] a = Table[ CoefficientList[n!*SeriesCoefficient[Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a]; Flatten[{{1}, {0}, {0, -1}, {0, -1}, {0, -1, 3}, {0, -1, 10}, {0, -1, 25, -15}, {0, -1, 56, -105}, {0, -1, 119, -490, \ 105}, {0, -1, 246, -1918, 1260}, {0, -1, 501, -6825, 9450, -945}}]
|
|
|
PROG
| (Maxima) T(n, k):=sum(binomial(n, k-j)*stirling2(n-k+j, j)*(-1)^(j), j, 0, k); [ From Vladimir Kruchinin, Jan 13 2012]
|
|
|
CROSSREFS
| Cf. A000587.
Sequence in context: A136239 A058175 A112906 * A145881 A135313 A022695
Adjacent sequences: A137372 A137373 A137374 * A137376 A137377 A137378
|
|
|
KEYWORD
| uned,tabl,sign
|
|
|
AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 09 2008
|
| |
|
|
