%I #7 Oct 17 2017 05:23:31
%S 1,6,63,392,1764,6352,19404,52272,127413,286286,601203,1192464,
%T 2252432,4078368,7116336,12018704,19718181,31521798,49228487,75274584,
%U 112911880,166423400,241382700,344962800,486301725,676932006,931282191,1267259168
%N Column 5 of triangle A123610.
%H G. C. Greubel, <a href="/A123615/b123615.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: P_5(x) / ((1-x)^2*(1-x^2)^2*(1-x^3)^2*(1-x^4)^2*(1-x^5)^2), with P_5(1) = 9!, where P_5(x) = (1+4*x+50*x^2+262*x^3+930*x^4+2566*x^5+5795*x^6+11156*x^7+ 18699*x^8+27712*x^9+36699*x^10+43696*x^11+46988*x^12+45696*x^13+ 40167*x^14+31828*x^15+22603*x^16+14268*x^17+7899*x^18+3762*x^19+ 1498*x^20+474*x^21+110*x^22+16*x^23+x^24).
%t CoefficientList[Series[(1 + 4*x + 50*x^2 + 262*x^3 + 930*x^4 + 2566*x^5 + 5795*x^6 + 11156*x^7 + 18699*x^8 + 27712*x^9 + 36699*x^10 + 43696*x^11 + 46988*x^12 + 45696*x^13 + 40167*x^14 + 31828*x^15 + 22603*x^16 + 14268*x^17 + 7899*x^18 + 3762*x^19 + 1498*x^20 + 474*x^21 + 110*x^22 + 16*x^23 + x^24)/((1 - x)^2*(1 - x^2)^2*(1 - x^3)^2*(1 - x^4)^2*(1 - x^5)^2), {x, 0, 50}], x] (* _G. C. Greubel_, Oct 16 2017 *)
%o (PARI) {a(n)=polcoeff(truncate(Ser([1,4,50,262,930,2566,5795,11156,18699,27712, 36699,43696,46988,45696,40167,31828,22603,14268,7899,3762,1498,474,110,16,1])) /((1-x)^2*(1-x^2)^2*(1-x^3)^2*(1-x^4)^2*(1-x^5)^2 +x*O(x^n)),n)}
%Y Cf. A123610 (triangle); columns: A005997, A123613, A123614, A123616.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Oct 03 2006