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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
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
Sequence in context: A306880 A128579 A194453 * A242105 A001046 A158257
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.)