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A059098 Triangle T(n,m) = Sum_{i=0..n} stirling2(n,i)*Product_{j=1..m} (i-j+1), m=0..n. 1
1, 1, 1, 2, 3, 2, 5, 10, 12, 6, 15, 37, 62, 60, 24, 52, 151, 320, 450, 360, 120, 203, 674, 1712, 3120, 3720, 2520, 720, 877, 3263, 9604, 21336, 33600, 34440, 20160, 5040, 4140, 17007, 56674, 147756, 287784, 394800, 352800, 181440, 40320, 21147, 94828 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

T(n,0)=A000110; T(n,1)=A005493. Row sums give A059099.

LINKS

Table of n, a(n) for n=0..46.

FORMULA

E.g.f. for T(n, m): (exp(x)-1)^m*(exp(exp(x)-1)).

T(n,m) = m!*A049020(n,m). - R. J. Mathar, May 17 2016

EXAMPLE

Triangle begins:

[1],

[1, 1],

[2, 3, 2],

[5, 10, 12, 6],

[15, 37, 62, 60, 24],

[52, 151, 320, 450, 360, 120], ...;

E.g.f. for T(n, 2) = (exp(x)-1)^2*(exp(exp(x)-1)) = x^2 + 2*x^3 + 31/12*x^4 + 8/3*x^5 + 107/45*x^6 + 343/180*x^7 + 28337/20160*x^8 + 349/360*x^9 + ...;

E.g.f. for T(n, 3) = (exp(x)-1)^3*(exp(exp(x)-1)) = x^3 + 5/2*x^4 + 15/4*x^5 + 13/3*x^6 + 127/30*x^7 + 1759/480*x^8 + 34961/12096*x^9 + ...

n-th row is M^n*[1,0,0,0,...], where M is a tridiagonal matrix with all 1's in the superdiagonal, (1,2,3,...) in the main and subdiagonals; and the rest zeros. - Gary W. Adamson, Jun 23 2011

CROSSREFS

Cf. A049020, A001861, A059099.

Sequence in context: A050159 A147294 A296662 * A082050 A183098 A183101

Adjacent sequences:  A059095 A059096 A059097 * A059099 A059100 A059101

KEYWORD

easy,nonn,tabl

AUTHOR

Vladeta Jovovic, Jan 02 2001

STATUS

approved

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Last modified October 21 12:44 EDT 2018. Contains 316420 sequences. (Running on oeis4.)