A382676 a(n) = Sum_{k=0..n} (k!)^2 * binomial(k+2,2) * Stirling2(n+1,k+1)^2.
1, 4, 52, 1372, 60316, 3964684, 363503932, 44280657292, 6913081723516, 1345238707327564, 319137578070718012, 90648956570718822412, 30369040605677566161916, 11848724306426305222109644, 5325560174867275152102351292, 2731649923185995549312271694732
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, k!^2*binomial(k+2, 2)*stirling(n+1, k+1, 2)^2);
Formula
a(n) = (n!)^2 * [(x*y)^n] exp(x+y) / (exp(x) + exp(y) - exp(x+y))^3.