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A256550 Triangle read by rows, T(n,k) = EL(n,k)/(n-k+1)! and EL(n,k) the matrix-exponential of the unsigned Lah numbers scaled by exp(-1), for n>=0 and 0<=k<=n. 1
1, 0, 1, 0, 1, 1, 0, 2, 3, 1, 0, 5, 12, 6, 1, 0, 15, 50, 40, 10, 1, 0, 52, 225, 250, 100, 15, 1, 0, 203, 1092, 1575, 875, 210, 21, 1, 0, 877, 5684, 10192, 7350, 2450, 392, 28, 1, 0, 4140, 31572, 68208, 61152, 26460, 5880, 672, 36, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Table of n, a(n) for n=0..54.

FORMULA

T(n+1,1) = Bell(n) = A000110(n).

T(n+2,2) = C(n+2,2)*Bell(n) = A105479(n+2).

T(n+1,n) = A000217(n).

T(n+2,n) = A008911(n+1).

EXAMPLE

Triangle starts:

1;

0,    1;

0,    1,    1;

0,    2,    3,    1;

0,    5,   12,    6,    1;

0,   15,   50,   40,   10,    1;

0,   52,  225,  250,  100,   15,   1;

0,  203, 1092, 1575,  875,  210,  21,  1;

PROG

(Sage)

def T(dim) :

    M = matrix(ZZ, dim)

    for n in range(dim) :

        M[n, n] = 1

        for k in range(n) :

            M[n, k] = (k*n*gamma(n)^2)/(gamma(k+1)^2*gamma(n-k+1))

    E = M.exp()/exp(1)

    for n in range(dim) :

        for k in range(n) :

            M[n, k] = E[n, k]/factorial(n-k+1)

    return M

T(8) # Computes the sequence as a lower triangular matrix.

CROSSREFS

Cf. A000110, A000217, A008911, A105479, A256551 (matrix inverse).

Sequence in context: A172380 A144633 A264428 * A005210 A264430 A264433

Adjacent sequences:  A256547 A256548 A256549 * A256551 A256552 A256553

KEYWORD

nonn,tabl,easy

AUTHOR

Peter Luschny, Apr 01 2015

STATUS

approved

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Last modified March 21 01:18 EDT 2019. Contains 321356 sequences. (Running on oeis4.)