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A255192 Triangle of number of connected subgraphs of K(n,n) with m edges. 1
1, 4, 1, 81, 78, 36, 9, 1, 4096, 8424, 9552, 7464, 4272, 1812, 560, 120, 16, 1, 390625, 1359640, 2696200, 3880300, 4394600, 4059000, 3111140, 1994150, 1070150, 478800, 176900, 53120, 12650, 2300, 300, 25, 1, 60466176, 314452800, 939988800, 2075760000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

m ranges from 2n-1 to n^2.

First column is A068087.

LINKS

Table of n, a(n) for n=1..39.

FORMULA

Sum(k>=0, T(n,k)*(-1)^k ) = A136126(2*n-1,n-1) = A092552(n+1), alternating row sums.

EXAMPLE

Triangle begins:

----|------------------------------------------------------------

n\m |  1 2 3 4  5  6    7    8    9   10   11   12  13  14 15 16

----|------------------------------------------------------------

1   |  1

2   |  - - 4 1

3   |  - - - - 81 78   36    9    1

4   |  - - - -  -  - 4096 8424 9552 7464 4272 1812 560 120 16  1

PROG

(Python)

a(n, m) = f(1, n, n, m) where

def f(x, a, b, k):

...if b == k == 0: return 1

...if b == 0 or k == 0: return 0

...if x == a:

......return sum(binom(a, n)*f(x, x, b-1, k-n) for n in range(1, a+1))

...return sum(binom(b, n)*f(x, x, n, k2)*f(n, b, a-x, k-k2) for n in range(1, b+1) for k2 in range(0, k+1))

CROSSREFS

Cf. A005333 (row sums?).

Sequence in context: A114917 A100864 A295178 * A299582 A211341 A280620

Adjacent sequences:  A255189 A255190 A255191 * A255193 A255194 A255195

KEYWORD

nonn,tabf

AUTHOR

Thomas Dybdahl Ahle, Feb 16 2015

STATUS

approved

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Last modified August 13 19:30 EDT 2020. Contains 336451 sequences. (Running on oeis4.)