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A059114 Triangle T(n,m)= Sum_{i=0..n} L'(n,i)*Product_{j=1..m} (i-j+1), m=0..n. 1
1, 1, 1, 3, 4, 2, 13, 21, 18, 6, 73, 136, 156, 96, 24, 501, 1045, 1460, 1260, 600, 120, 4051, 9276, 15030, 16320, 11160, 4320, 720, 37633, 93289, 170142, 219450, 192360, 108360, 35280, 5040, 394353, 1047376, 2107448, 3116736, 3294480, 2405760 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

L'(n,i) are unsigned Lah numbers (Cf. A008297):L'(n,i)=n!/i!*binomial(n-1,i-1) for i >= 1, L'(0,0)=1, L'(n,0)=0 for n>0.T(n,0)=A000262(n); T(n,2)=A052852(n). Row sums give A059115.

LINKS

Table of n, a(n) for n=0..41.

FORMULA

E.g.f. for T(n, m)=(x/(1-x))^m*e^(x/(x-1)).

EXAMPLE

[1], [1, 1], [3, 4, 2], [13, 21, 18, 6], [73, 136, 156, 96, 24], [501, 1045, 1460, 1260, 600, 120], ...; E.g.f. for T(n, 2) = (x/(1-x))^2*e^(x/(x-1)) = x^2 + 3*x^3 + 13/2*x^4 + 73/6*x^5 + 167/8*x^6 + 4051/120*x^7 + ...

CROSSREFS

Cf. A059110, A052897.

Sequence in context: A019474 A072565 A159672 * A246322 A166074 A225475

Adjacent sequences:  A059111 A059112 A059113 * A059115 A059116 A059117

KEYWORD

easy,nonn,tabl

AUTHOR

Vladeta Jovovic, Jan 04 2001

STATUS

approved

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Last modified July 21 19:13 EDT 2019. Contains 325199 sequences. (Running on oeis4.)