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A304311 Triangle T(n,k) read by rows: number of bicolored connected graphs with n nodes and k nodes of the first color. 5
1, 1, 1, 1, 1, 1, 2, 3, 3, 2, 6, 11, 16, 11, 6, 21, 58, 98, 98, 58, 21, 112, 407, 879, 1087, 879, 407, 112, 853, 4306, 11260, 17578, 17578, 11260, 4306, 853, 11117, 72489, 230505, 436371, 537272, 436371, 230505, 72489, 11117 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..1274

FORMULA

T(n,k) = T(n,n-k).

EXAMPLE

Triangle begins

      1;

      1,     1;

      1,     1,      1;

      2,     3,      3,      2;

      6,    11,     16,     11,      6;

     21,    58,     98,     98,     58,     21;

    112,   407,    879,   1087,    879,    407,    112;

    853,  4306,  11260,  17578,  17578,  11260,   4306,   853;

  11117, 72489, 230505, 436371, 537272, 436371, 230505, 72489, 11117;

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) = {sum(i=2, #v, sum(j=1, i-1, gcd(v[i], v[j]))) + sum(i=1, #v, v[i]\2)}

S(n, y)={my(s=0); forpart(p=n, s+=permcount(p)*2^edges(p)*prod(i=1, #p, 1+y^p[i])); s/n!}

InvEulerMT(u)={my(n=#u, p=log(1+x*Ser(u)), vars=variables(p)); Vec(sum(i=1, n, moebius(i)*substvec(p + O(x*x^(n\i)), vars, apply(v->v^i, vars))/i) )}

{my(A=InvEulerMT(vector(10, n, S(n, y)))); for(n=0, #A, for(k=0, n, print1(polcoeff(if(n, A[n], 1), k), ", ")); print)} \\ Andrew Howroyd, May 13 2018

CROSSREFS

Cf. A054921 (row sums), A001349 (1st column), A126100 (2nd column), A303831 (3rd column), A294783 (trees).

Sequence in context: A328484 A319442 A299772 * A175393 A184829 A338307

Adjacent sequences:  A304308 A304309 A304310 * A304312 A304313 A304314

KEYWORD

nonn,tabl

AUTHOR

R. J. Mathar, May 10 2018

STATUS

approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)