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A202190 Triangle T(n,m) = coefficient of x^n in expansion of [x*(x+1)^(x+1)]^m = sum(n>=m, T(n,m) x^n*m!/n!). 0
1, 2, 1, 6, 6, 1, 12, 36, 12, 1, 40, 180, 120, 20, 1, 60, 960, 1020, 300, 30, 1, 378, 4620, 8400, 3780, 630, 42, 1, -336, 24864, 65520, 44240, 10920, 1176, 56, 1, 8496, 114912, 512568, 488880, 171360, 26712, 2016, 72, 1, -51120, 679680, 3885840, 5261760 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..49.

FORMULA

T(n,m):=(n)!/(m)!*sum(k=0..n-m, k!*sum(i=k..n-m, (stirling1(i,k)*binomial(k,n-i-m))/i!)*m^k/k!).

EXAMPLE

1

2, 1,

6, 6, 1,

12, 36, 12, 1,

40, 180, 120, 20, 1,

60, 960, 1020, 300, 30, 1,

378, 4620, 8400, 3780, 630, 42, 1

PROG

(Maxima)

T(n, m):=(n)!/(m)!*sum(k!*sum((stirling1(i, k)*binomial(k, n-i-m))/i!, i, k, n-m)*m^k/k!, k, 0, n-m);

CROSSREFS

Sequence in context: A259569 A046651 A063007 * A089231 A052296 A019538

Adjacent sequences:  A202187 A202188 A202189 * A202191 A202192 A202193

KEYWORD

sign,tabl

AUTHOR

Vladimir Kruchinin, Dec 14 2011

STATUS

approved

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Last modified October 22 05:06 EDT 2018. Contains 316432 sequences. (Running on oeis4.)