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A075525 Triangle T(n,k) defined by Sum_{1<=k<=n} T(n,k)*u^k*t^n/n! = ((1+t)*(1+t^2)*(1+t^3)...)^u. 2
1, 1, 1, 8, 3, 1, 6, 35, 6, 1, 144, 110, 95, 10, 1, 480, 1594, 585, 205, 15, 1, 5760, 8064, 8974, 1995, 385, 21, 1, 5040, 125292, 70252, 35329, 5320, 658, 28, 1, 524160, 684144, 1178540, 392364, 110649, 12096, 1050, 36, 1, 2177280, 14215536 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Also the Bell transform of A265024. For the definition of the Bell transform see A264428. - Peter Luschny, Jan 26 2016

LINKS

Table of n, a(n) for n=1..47.

FORMULA

Row sums give n!*A000009(n).

EXAMPLE

1; 1,1; 8,3,1; 6,35,6,1; 144,110,95,10,1;...

MAPLE

# Adds (1, 0, 0, 0, ...) as row 0.

seq(PolynomialTools[CoefficientList](n!*coeff(series(mul((1+z^k)^u, k=1..20), z, 20), z, n), u), n=0..9); # Peter Luschny, Jan 26 2016

PROG

(Sage)

# The function bell_matrix is defined in A264428.

# Adds (1, 0, 0, 0, ..) as row 0.

d = lambda n: sum((-1)^(d+1)*n/d for d in divisors(n))

bell_matrix(lambda n: factorial(n)*d(n+1), 9) # Peter Luschny, Jan 26 2016

CROSSREFS

Cf. A008298.

Sequence in context: A092555 A001061 A259073 * A242048 A097890 A088453

Adjacent sequences:  A075522 A075523 A075524 * A075526 A075527 A075528

KEYWORD

nonn,tabl

AUTHOR

Vladeta Jovovic, Oct 11 2002

STATUS

approved

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Last modified January 22 05:11 EST 2019. Contains 319353 sequences. (Running on oeis4.)