A151643 generating functions and recurrence Generating function: Sum_{n=0..oo} a(n)*x^n = 16*x^3*(529 + 694270*x + 21103855*x^2 - 8186379610*x^3 + 256740749011*x^4 + 4302657488870*x^5 - 303288466811925*x^6 + 4374822531326750*x^7 - 10203282324594375*x^8 - 287980495540093750*x^9 + 2658292808231578125*x^10 - 7508437128370468750*x^11 + 196662938562890625*x^12 + 46458011150113281250*x^13 - 99410281104052734375*x^14 + 35183351447753906250*x^15 + 75091538781738281250*x^16 + 6514353808593750000*x^17)/( Product_{j=0..5} (1 - binomial(j+4,4)*x)^(6-j) ). Exponential generating function: Sum_{n=0..oo} a(n)*x^n/n! = exp(126*x) - (1 + 280*x)*exp(70*x) + 350*x*(1 + 28*x)*exp(35*x) - 150*x*(1 + 48*x + 240*x^2)*exp(15*x) + (25/3)*x*(3 + 174*x + 880*x^2 + 800*x^3)*exp(5*x) - (1/15)*x*(15 + 930*x + 2280*x^2 + 1120*x^3 + 128*x^4)*exp(x). Recurrence: a(n) = 462*a(n-1) - 91531*a(n-2) + 10359990*a(n-3) - 751926160*a(n-4) + 37211988696*a(n-5) - 1302889937812*a(n-6) + 33041329661136*a(n-7) - 616216166660230*a(n-8) + 8532037831808700*a(n-9) - 88161849837783250*a(n-10) + 681071135526667500*a(n-11) - 3928678356172712500*a(n-12) + 16849648606559250000*a(n-13) - 53333569862180312500*a(n-14) + 123260625734287500000*a(n-15) - 205051485813712890625*a(n-16) + 240815404573652343750*a(n-17) - 193749765819873046875*a(n-18) + 101292345769042968750*a(n-19) - 30943180590820312500*a(n-20) + 4187798876953125000*a(n-21).