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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 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 December 3 01:25 EST 2022. Contains 358510 sequences. (Running on oeis4.)