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 A322278 Triangle read by rows: T(n,k) is the number of k-colored connected graphs on n labeled nodes up to permutation of the colors. 7
 1, 0, 1, 0, 3, 4, 0, 19, 84, 38, 0, 195, 2470, 3140, 728, 0, 3031, 108390, 307390, 186360, 26704, 0, 67263, 7192444, 42747460, 52630060, 18926544, 1866256, 0, 2086099, 726782784, 9030799218, 20784069600, 14401134944, 3463311488, 251548592 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Equivalently, the number of ways to choose a stable partition of a simple connected graph on n labeled nodes with k parts. See A322064 for the definition of stable partition. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1275 FORMULA T(n,k) = (1/k!)*Sum_{j=0..k} (-1)^(k-j)*binomial(k,j)*A322279(n,j). EXAMPLE Triangle begins: 1; 0, 1; 0, 3, 4; 0, 19, 84, 38; 0, 195, 2470, 3140, 728; 0, 3031, 108390, 307390, 186360, 26704; 0, 67263, 7192444, 42747460, 52630060, 18926544, 1866256; ... PROG (PARI) M(n, K=n)={ my(p=sum(j=0, n, x^j/(j!*2^binomial(j, 2))) + O(x*x^n)); my(q=sum(j=0, n, x^j*2^binomial(j, 2)) + O(x*x^n)); my(W=vector(K, k, Col(serlaplace(log(serconvol(q, p^k)))))); Mat(vector(K, k, sum(i=1, k, (-1)^(k-i)*binomial(k, i)*W[i])/k!)); } my(T=M(7)); for(n=1, #T, print(T[n, 1..n])) CROSSREFS Row sums are A322064. Columns k=2..4 are A001832(for n > 1), A322330, A322331. Right diagonal is A001187. Cf. A058843, A058875, A322279, A322280. Sequence in context: A078067 A192442 A009126 * A102222 A171657 A287696 Adjacent sequences: A322275 A322276 A322277 * A322279 A322280 A322281 KEYWORD nonn,tabl AUTHOR Andrew Howroyd, Dec 01 2018 STATUS approved

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Last modified May 22 17:21 EDT 2024. Contains 372758 sequences. (Running on oeis4.)