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 A295384 a(n) = n!*Sum_{k=0..n} (-1)^k*binomial(2*n,n-k)*n^k/k!. 2
 1, 1, 0, -15, -112, -135, 9504, 152425, 610560, -27692847, -765107200, -6289891839, 213472972800, 9380264146825, 129378550468608, -3294028613874375, -226623617585053696, -4707649131227927775, 83803818828756418560, 9446689798312021406353, 277055229100887244800000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS G. C. Greubel, Table of n, a(n) for n = 0..400 Eric Weisstein's World of Mathematics, Laguerre Polynomial Wikipedia, Laguerre polynomials FORMULA a(n) = n! * [x^n] exp(-n*x/(1 - x))/(1 - x)^(n+1). a(n) = n!*Laguerre(n,n,n). MATHEMATICA Table[n! SeriesCoefficient[Exp[-n x/(1 - x)]/(1 - x)^(n + 1), {x, 0, n}], {n, 0, 20}] Table[n! LaguerreL[n, n, n], {n, 0, 20}] Table[(-1)^n HypergeometricU[-n, n + 1, n], {n, 0, 20}] Join[{1}, Table[n! Sum[(-1)^k Binomial[2 n, n - k] n^k/k!, {k, 0, n}], {n, 1, 20}]] PROG (PARI) for(n=0, 30, print1(n!*sum(k=0, n, (-1)^k*binomial(2*n, n-k)*n^k/k!), ", ")) \\ G. C. Greubel, Feb 06 2018 (MAGMA) [Factorial(n)*(&+[(-1)^k*Binomial(2*n, n-k)*n^k/Factorial(k): k in [0..n]]): n in [0..30]]; // G. C. Greubel, Feb 06 2018 CROSSREFS Cf. A006902, A277373, A277423, A295385. Sequence in context: A105051 A105040 A298123 * A110822 A222410 A001849 Adjacent sequences:  A295381 A295382 A295383 * A295385 A295386 A295387 KEYWORD sign AUTHOR Ilya Gutkovskiy, Nov 21 2017 STATUS approved

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Last modified April 5 20:22 EDT 2020. Contains 333260 sequences. (Running on oeis4.)