login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A144303 Square array A(n,m), n>=0, m>=0, read by antidiagonals: A(n,m) = n-th number of the m-th iteration of the hyperbinomial transform on the sequence of 1's. 12
1, 1, 1, 1, 2, 1, 1, 3, 6, 1, 1, 4, 13, 29, 1, 1, 5, 22, 81, 212, 1, 1, 6, 33, 163, 689, 2117, 1, 1, 7, 46, 281, 1564, 7553, 26830, 1, 1, 8, 61, 441, 2993, 18679, 101961, 412015, 1, 1, 9, 78, 649, 5156, 38705, 268714, 1639529, 7433032, 1, 1, 10, 97, 911, 8257, 71801, 592489, 4538209, 30640257, 154076201, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

See A088956 for the definition of the hyperbinomial transform.

A(n,m), n>=0, m>=0, is the number of subtrees of the complete graph K_{n+m} on n+m vertices containing a given, fixed subtree on m vertices. - Alex Chin, Jul 25 2013

LINKS

Alois P. Heinz, Rows n = 0..140, flattened

N. J. A. Sloane, Transforms

FORMULA

E.g.f. of column k: exp(x) * (-LambertW(-x)/x)^k.

A(n,k) = Sum_{j=0..n} k * (n-j+k)^(n-j-1) * C(n,j).

EXAMPLE

Square array begins:

  1,     1,      1,      1,      1,       1,       1, ...

  1,     2,      3,      4,      5,       6,       7, ...

  1,     6,     13,     22,     33,      46,      61, ...

  1,    29,     81,    163,    281,     441,     649, ...

  1,   212,    689,   1564,   2993,    5156,    8257, ...

  1,  2117,   7553,  18679,  38705,   71801,  123217, ...

  1, 26830, 101961, 268714, 592489, 1166886, 2120545, ...

MAPLE

hymtr:= proc(p) proc(n, m) `if`(m=0, p(n), m*add(

           p(k)*binomial(n, k) *(n-k+m)^(n-k-1), k=0..n))

        end end:

A:= hymtr(1):

seq(seq(A(n, d-n), n=0..d), d=0..12);

MATHEMATICA

a[_, 0] = 1; a[n_, k_] := Sum[k*(n - j + k)^(n - j - 1)*Binomial[n, j], {j, 0, n}]; Table[a[n - k, k], {n, 0, 10}, {k, n, 0, -1}] // Flatten (* Jean-Fran├žois Alcover, Jun 24 2013 *)

CROSSREFS

Columns m=0-10 give: A000012, A088957, A089461, A089464, A218496, A218497, A218498, A218499, A218500, A218501, A218502.

Rows n=0-2 give: A000012, A000027, A028872.

Main diagonal gives A252766.

Cf. A007318, A088956.

Sequence in context: A128325 A307883 A111528 * A287024 A107702 A174480

Adjacent sequences:  A144300 A144301 A144302 * A144304 A144305 A144306

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Sep 17 2008, revised Oct 30 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 27 15:59 EST 2020. Contains 332307 sequences. (Running on oeis4.)