proposed

approved

editing

proposed

Andrew Howroyd, <a href="/A007719/b007719.txt">Table of n, a(n) for n = 0..50</a>

Row sums of A322115.

approved

editing

proposed

approved

editing

proposed

EULERi[b_] := Module[{a, c, i, d}, c = {}; For[i = 1, i <= Length[b], i++,

c = Append[c, i*b[[i]] - Sum[c[[d]]*b[[i - d]], {d, 1, i - 1}]]]; a = {};

Module[{a, c, i, d}, c = {}; For[i = 1, i <= Length[b], i++, a = Append[a, (1/i)*Sum[mob[i, d]*c[[d]], {d, 1, i}]]]; Return[a]];

c permcount[v_] := Module[{m = 1, s = 0, k = Append0, t}, For[c, i*b[[ = 1, i]] - Sum[c[ <= Length[d]v]*b, i++, t = v[[i - d]], {d, ; k = If[i > 1, && t == v[[i - 1}]], k + 1, 1]; m *= t k; s += t]; s!/m];

a = {};

For[i = 1, i <= Length[b], i++, a = Append[a, (1/i)*

Sum[mobKq[i, dq_, t_, k_]*c := SeriesCoefficient[1/Product[g = GCD[t, q[[dj]]], {d, ; (1, i}] - x^(q[[j]]; Return/g))^g, {j, 1, Length[aq]}], {x, 0, k}];

RowSumMats[n_, m_, k_] := Module[{s = 0}, Do[s += permcount[v_q] := Module* SeriesCoefficient[ Exp[Sum[Kq[q, t, k]/t x^t, {m = t, 1, s = 0, k = n}]], {x, 0, tn}], {q, IntegerPartitions[m]}, ]; s/m!];

For[i = 1, i <= Length[v], i++, t = v[[i]]; k =

If[i > 1 && t == v[[i - 1]], k + 1, 1]; m *= t k; s += t]; s!/m];

Kq[q_, t_, k_] := SeriesCoefficient[1/Product[g =

GCD[t, q[[j]]]; (1 - x^(q[[j]]/g))^g, {j, 1, Length[q]}], {x,

0, k}];

RowSumMats[n_, m_, k_] := Module[{s = 0}, Do[s += permcount[q]*

SeriesCoefficient[Exp[Sum[Kq[q, t, k]/t x^t, {t, 1, n}]],

{x, 0, n}], {q, IntegerPartitions[m]}]; s/m!];

mob[m_, n_] := If[Mod[m, n] == 0, MoebiusMu[m/n], 0];

EULERi[b_] :=

Module[{a, c, i, d}, c = {}; For[i = 1, i <= Length[b], i++,

c = Append[c, i*b[[i]] - Sum[c[[d]]*b[[i - d]], {d, 1, i - 1}]]];

a = {};

For[i = 1, i <= Length[b], i++, a = Append[a, (1/i)*

Sum[mob[i, d]*c[[d]], {d, 1, i}]]]; Return[a]];

permcount[v_] := Module[{m = 1, s = 0, k = 0, t},

For[i = 1, i <= Length[v], i++, t = v[[i]]; k =

If[i > 1 && t == v[[i - 1]], k + 1, 1]; m *= t k; s += t]; s!/m];

Kq[q_, t_, k_] := SeriesCoefficient[1/Product[g =

GCD[t, q[[j]]]; (1 - x^(q[[j]]/g))^g, {j, 1, Length[q]}], {x,

0, k}];

RowSumMats[n_, m_, k_] := Module[{s = 0}, Do[s += permcount[q]*

SeriesCoefficient[Exp[Sum[Kq[q, t, k]/t x^t, {t, 1, n}]],

{x, 0, n}], {q, IntegerPartitions[m]}]; s/m!];

A007717 = Table[Print[n]; RowSumMats[n, 2 n, 2], {n, 0, 20}];

Join[{1}, EULERi[Rest[A007717]]] (* Jean-François Alcover, Oct 29 2018, using Andrew Howroyd's code for A007717 *)

approved

editing

proposed

approved

editing

proposed

R. J. Mathar, <a href="http://arxiv.org/abs/1709.09000">Statistics on Small Graphs</a>, arXiv:1709.09000 [math.CO] (2017) Table 63.

proposed

editing