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 A138107 Infinite square array: T(n,k) = number of directed multigraphs with loops with n arcs and k vertices; read by falling antidiagonals. 13
 1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 2, 6, 1, 0, 1, 2, 10, 10, 1, 0, 1, 2, 11, 31, 19, 1, 0, 1, 2, 11, 47, 90, 28, 1, 0, 1, 2, 11, 51, 198, 222, 44, 1, 0, 1, 2, 11, 52, 269, 713, 520, 60, 1, 0, 1, 2, 11, 52, 291, 1270, 2423, 1090, 85, 1, 0, 1, 2, 11, 52, 295, 1596, 5776, 7388, 2180, 110, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Partial sums of the rows of A136564. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..1325 R. J. Mathar, Statistics on Small Graphs, arXiv:1709.09000 (2017) Table 79. FORMULA T(n,k) = Sum_{p=0..k} A136564(n,p). If k >= 2n, T(n,k) = A052171(n). EXAMPLE The array begins:    1, 1,  1,    1,     1,     1,     1,     1,     1,...    0, 1,  2,    2,     2,     2,     2,     2,     2,...    0, 1,  6,   10,    11,    11,    11,    11,    11,...    0, 1, 10,   31,    47,    51,    52,    52,    52,...    0, 1, 19,   90,   198,   269,   291,   295,   296,  296...    0, 1, 28,  222,   713,  1270,  1596,  1697,  1719, 1723...    0, 1, 44,  520,  2423,  5776,  8838, 10425, 10922,...    0, 1, 60, 1090,  7388, 24032, 46384, ...    0, 1, 85, 2180, 21003, 93067, ..    0, 1,110, 4090,...    ... PROG (PARI) permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m} edges(v, t) = {prod(i=2, #v, prod(j=1, i-1, my(g=gcd(v[i], v[j])); t(v[i]*v[j]/g)^(2*g))) * prod(i=1, #v, t(v[i])^v[i])} G(n, x)={my(s=0); forpart(p=n, s+=permcount(p)/edges(p, i->1-x^i)); s/n!} T(n)={Mat(vector(n+1, k, Col(O(y*y^n) + G(k-1, y + O(y*y^n)))))} {my(A=T(10)); for(n=1, #A, print(A[n, ]))} \\ Andrew Howroyd, Oct 22 2019 CROSSREFS Columns k=0..4 are: A000007, A000012, A005993, A050927, A050929. Cf. A052171, A136564, A333361. Sequence in context: A138352 A129620 A074766 * A089631 A332032 A298878 Adjacent sequences:  A138104 A138105 A138106 * A138108 A138109 A138110 KEYWORD nonn,tabl AUTHOR Benoit Jubin, May 03 2008 EXTENSIONS More terms from Vladeta Jovovic and Benoit Jubin, Sep 10 2008 STATUS approved

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Last modified January 26 22:05 EST 2022. Contains 350601 sequences. (Running on oeis4.)