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 A295406 a(n) = n! * Laguerre(n, 2*n, -n). 7
 1, 4, 58, 1422, 49000, 2174360, 118023264, 7574532826, 561071549056, 47111034709260, 4421715905632000, 458741213603157254, 52129735913348001792, 6439324687323193520608, 859089518697047400878080, 123108032319553206480143250, 18858657171509448248927617024 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..300 Eric Weisstein's World of Mathematics, Laguerre Polynomial Wikipedia, Laguerre polynomials FORMULA a(n) = n!*Sum_{k=0..n} binomial(3*n,n-k)*n^k/k!. a(n) ~ sqrt(1/2 + 5/(2*sqrt(13))) * ((11 + sqrt(13))/2)^n * exp((sqrt(13)-5)*n/2) * n^n. a(n) = n! * [x^n] exp(n*x/(1 - x))/(1 - x)^(2*n+1). - Ilya Gutkovskiy, Nov 23 2017 MATHEMATICA Table[n!*LaguerreL[n, 2*n, -n], {n, 0, 15}] Join[{1}, Table[n!*Sum[Binomial[3*n, n-k]*n^k/k!, {k, 0, n}], {n, 1, 15}]] PROG (PARI) for(n=0, 30, print1(n!*sum(k=0, n, binomial(3*n, n-k)*n^k/k!), ", ")) \\ G. C. Greubel, Feb 06 2018 (MAGMA) [Factorial(n)*(&+[Binomial(3*n, n-k)*n^k/Factorial(k): k in [0..n]]): n in [0..30]]; // G. C. Greubel, Feb 06 2018 CROSSREFS Cf. A277373, A295385, A295407, A295408. Sequence in context: A240430 A216795 A216352 * A229528 A109056 A326944 Adjacent sequences:  A295403 A295404 A295405 * A295407 A295408 A295409 KEYWORD nonn AUTHOR Vaclav Kotesovec, Nov 22 2017 STATUS approved

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Last modified April 3 04:21 EDT 2020. Contains 333195 sequences. (Running on oeis4.)