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A178831 Rectangular array T(n,k)=Binomial(n+1,2)*(n^k-(n-1)^k) read by antidiagonals . 0
1, 1, 3, 1, 9, 6, 1, 21, 30, 10, 1, 45, 114, 70, 15, 1, 93, 390, 370, 135, 21, 1, 189, 1266, 1750, 915, 231, 28 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

T(n,k)is the sum of the elements in the image sets of all functions f:{1,2,...,k}->{1,2,...,n}.

Equivalently, the sum of the distinct entries in each length k sequence on {1,2,...,n}.

LINKS

Table of n, a(n) for n=1..28.

FORMULA

E.g.f. for row n:Binomial(n+1,2)exp((n-1)x)(exp(x)-1)

EXAMPLE

  1,  1,   1,   1,     1,     1,...

  3,  9,  21,   45,    93,    189,...

  6,  30, 114,  390,   1266,  3990,...

  10, 70, 370,  1750,  7810,  33670,...

  15, 135, 915, 5535,  31515, 172935,...

  21, 231, 1911, 14091,97671, 651651,..

MATHEMATICA

Table[Range[7]! Rest[CoefficientList[Series[Binomial[n+1, 2] Exp[(n-1)x](Exp[x]-1), {x, 0, 7}], x]], {n, 1, 7}]//Grid

CROSSREFS

Cf. A068156 the case for n=2.

Sequence in context: A132819 A264364 A105545 * A164942 A027465 A236420

Adjacent sequences:  A178828 A178829 A178830 * A178832 A178833 A178834

KEYWORD

nonn,tabl

AUTHOR

Geoffrey Critzer, Dec 27 2010

STATUS

approved

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Last modified September 25 19:48 EDT 2017. Contains 292500 sequences.