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 A335310 a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n+k,k) * (-n)^(n-k). 3
 1, 1, -2, 11, -74, 477, -804, -84425, 3315334, -102211207, 3005297956, -88338323709, 2627003399164, -78764141488043, 2341929797646648, -66394419743289105, 1609460569459689286, -18001777147777896975, -1625299659961386724524, 196005371138608184827003 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..386 FORMULA a(n) = central coefficient of (1 - (n - 2)*x - (n - 1)*x^2)^n. a(n) = [x^n] 1 / sqrt(1 + 2*(n - 2)*x + n^2*x^2). a(n) = n! * [x^n] exp((2 - n)*x) * BesselI(0,2*sqrt(1 - n)*x). a(n) = Sum_{k=0..n} binomial(n,k)^2 * (1-n)^k. MATHEMATICA Join[{1}, Table[Sum[Binomial[n, k] Binomial[n + k, k] (-n)^(n - k), {k, 0, n}], {n, 1, 19}]] Table[SeriesCoefficient[1/Sqrt[1 + 2 (n - 2) x + n^2 x^2], {x, 0, n}], {n, 0, 19}] Table[n! SeriesCoefficient[Exp[(2 - n) x] BesselI[0, 2 Sqrt[1 - n] x], {x, 0, n}], {n, 0, 19}] Table[Hypergeometric2F1[-n, -n, 1, 1 - n], {n, 0, 19}] PROG (PARI) a(n) = sum(k=0, n, binomial(n, k)^2*(1-n)^k); \\ Michel Marcus, Jun 01 2020 CROSSREFS Cf. A098332, A116091, A126869, A307884, A307885, A331657, A335309. Sequence in context: A049671 A074609 A299786 * A199417 A114179 A231556 Adjacent sequences: A335307 A335308 A335309 * A335311 A335312 A335313 KEYWORD sign AUTHOR Ilya Gutkovskiy, May 31 2020 STATUS approved

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Last modified December 7 11:41 EST 2023. Contains 367656 sequences. (Running on oeis4.)