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 A354941 a(n) = Sum_{k=0..n} binomial(n,k)^3 * k! * (-2)^(n-k). 2
 1, -1, -10, -2, 488, 4088, -9968, -730480, -9751936, -11540096, 2480655104, 62522038016, 680469314560, -8292439149568, -606011029669888, -15765339965278208, -183530875864317952, 4164677242501038080, 318357069130977181696, 10359690304436314505216, 176911847384965046337536 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..20. FORMULA Sum_{n>=0} a(n) * x^n / n!^3 = BesselI(0,2*sqrt(x)) * Sum_{n>=0} (-2)^n * x^n / n!^3. MATHEMATICA Table[Sum[Binomial[n, k]^3 k! (-2)^(n - k), {k, 0, n}], {n, 0, 20}] nmax = 20; CoefficientList[Series[BesselI[0, 2 Sqrt[x]] Sum[(-2)^k x^k/k!^3, {k, 0, nmax}], {x, 0, nmax}], x] Range[0, nmax]!^3 PROG (PARI) a(n) = sum(k=0, n, binomial(n, k)^3 * k! * (-2)^(n-k)); \\ Michel Marcus, Jun 12 2022 CROSSREFS Cf. A000023, A274246, A295382, A343840, A354942. Sequence in context: A178643 A038304 A290308 * A352689 A159005 A144859 Adjacent sequences: A354938 A354939 A354940 * A354942 A354943 A354944 KEYWORD sign AUTHOR Ilya Gutkovskiy, Jun 12 2022 STATUS approved

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Last modified August 13 16:51 EDT 2024. Contains 375144 sequences. (Running on oeis4.)