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%I #7 Oct 17 2017 05:23:23
%S 1,7,100,786,4420,19404,71188,226512,644231,1670015,4008200,9009728,
%T 19146090,38744496,75117600,140218218,253051227,443056383,754838884,
%U 1254576400,2038689796,3245256396,5069041432,7780827600,11752298725
%N Column 6 of triangle A123610.
%H G. C. Greubel, <a href="/A123616/b123616.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: P_6(x) / ((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6))^2, with P_6(1) = 11!, where P_6(x) = (1+5*x+85*x^2+581*x^3+2763*x^4+9987*x^5+29644*x^6+74546*x^7+ 164629*x^8+324255*x^9+579250*x^10+946960*x^11+1429875*x^12+2003713*x^13+ 2620218*x^14+3205496*x^15+3679773*x^16+3967701*x^17+4024087*x^18+ 3837087*x^19+3440204*x^20+2894878*x^21+2283089*x^22+1681653*x^23+ 1153208*x^24+731684*x^25+427027*x^26+226843*x^27+108486*x^28+45806*x^29+ 16737*x^30+5073*x^31+1221*x^32+211*x^33+23*x^34+x^35).
%o (PARI) {a(n)=polcoeff(truncate(Ser([1,5,85,581,2763,9987,29644,74546,164629, 324255,579250,946960,1429875,2003713,2620218,3205496,3679773,3967701, 4024087,3837087,3440204,2894878,2283089,1681653,1153208,731684,427027, 226843,108486,45806,16737,5073,1221,211,23,1])) / ((1-x)^2*(1-x^2)^2*(1-x^3)^2*(1-x^4)^2*(1-x^5)^2*(1-x^6)^2 +x*O(x^n)),n)}
%Y Cf. A123610 (triangle); columns: A005997, A123613, A123614, A123615.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Oct 03 2006
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