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A202184
Triangle T(n,m) = coefficient of x^n in expansion of x^m*(x+1)^(m*x^2) = sum(n>=m, T(n,m) x^n*m!/n!).
0
1, 0, 1, 0, 0, 1, 24, 0, 0, 1, -60, 120, 0, 0, 1, 240, -360, 360, 0, 0, 1, 1260, 1680, -1260, 840, 0, 0, 1, -12096, 30240, 6720, -3360, 1680, 0, 0, 1, 105840, -290304, 226800, 20160, -7560, 3024, 0, 0, 1, -388800, 2721600, -2358720, 1058400, 50400, -15120
OFFSET
1,7
COMMENTS
1
FORMULA
T(n,m):=n!/m!*sum(k=0..(n-m)/2, (m^k*stirling1(n-m-2*k,k))/(n-m-2*k)!).
EXAMPLE
1,
0, 1,
0, 0, 1,
24, 0, 0, 1,
-60, 120, 0, 0, 1,
240, -360, 360, 0, 0, 1,
1260, 1680, -1260, 840, 0, 0, 1
PROG
(Maxima)
T(n, m):=n!/m!*sum((m^k*stirling1(n-m-2*k, k))/(n-m-2*k)!, k, 0, (n-m)/2);
CROSSREFS
Sequence in context: A140793 A023923 A267334 * A368027 A357967 A353227
KEYWORD
sign,tabl
AUTHOR
Vladimir Kruchinin, Dec 13 2011
STATUS
approved