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 A346258 E.g.f.: exp(x) / (1 - 3 * x)^(1/3). 3
 1, 2, 7, 44, 421, 5366, 84907, 1601552, 35052649, 872931626, 24368595631, 753607111412, 25572085243597, 944609383245854, 37731673388579731, 1620520035001182296, 74466516342569480017, 3645540855448417250642, 189415873005295070803159, 10410429682102309433442236 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A007559. LINKS Table of n, a(n) for n=0..19. FORMULA a(n) = Sum_{k=0..n} binomial(n,k) * A007559(k). a(n) ~ n! * exp(1/3) * 3^n / (Gamma(1/3) * n^(2/3)). - Vaclav Kotesovec, Aug 14 2021 a(n+2) = (3*n+5)*a(n+1)-3*(n+1)*a(n). - Tani Akinari, Sep 08 2023 MAPLE g:= proc(n) option remember; `if`(n<2, 1, (3*n-2)*g(n-1)) end: a:= n-> add(binomial(n, k)*g(k), k=0..n): seq(a(n), n=0..19); # Alois P. Heinz, Aug 10 2021 MATHEMATICA nmax = 19; CoefficientList[Series[Exp[x]/(1 - 3 x)^(1/3), {x, 0, nmax}], x] Range[0, nmax]! Table[Sum[Binomial[n, k] 3^k Pochhammer[1/3, k], {k, 0, n}], {n, 0, 19}] Table[HypergeometricU[1/3, n + 4/3, 1/3]/3^(1/3), {n, 0, 19}] PROG (Maxima) a[n]:=if n<2 then n+1 else (3*n-1)*a[n-1]+3*(1-n)*a[n-2]; makelist(a[n], n, 0, 50); /* Tani Akinari, Sep 08 2023 */ CROSSREFS Cf. A000522, A007559, A010845, A033030, A084262, A347012, A347013, A347014. Sequence in context: A306880 A128579 A194453 * A242105 A001046 A158257 Adjacent sequences: A346255 A346256 A346257 * A346259 A346260 A346261 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Aug 10 2021 STATUS approved

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Last modified April 19 16:52 EDT 2024. Contains 371794 sequences. (Running on oeis4.)