A346258 E.g.f.: exp(x) / (1 - 3 * x)^(1/3).

1, 2, 7, 44, 421, 5366, 84907, 1601552, 35052649, 872931626, 24368595631, 753607111412, 25572085243597, 944609383245854, 37731673388579731, 1620520035001182296, 74466516342569480017, 3645540855448417250642, 189415873005295070803159, 10410429682102309433442236

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