The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A365569 Expansion of e.g.f. 1 / (6 - 5 * exp(x))^(3/5). 5

%I #18 Nov 16 2023 11:51:10

%S 1,3,27,387,7659,193491,5948091,215446563,8984708235,423944899443,

%T 22328393101659,1298429924941251,82625791930962219,

%U 5711012035686681363,426058604580805219323,34121803137713388036963,2919847869159667841599947,265868538017899566748612275

%N Expansion of e.g.f. 1 / (6 - 5 * exp(x))^(3/5).

%F a(n) = Sum_{k=0..n} (Product_{j=0..k-1} (5*j+3)) * Stirling2(n,k).

%F a(0) = 1; a(n) = Sum_{k=1..n} (5 - 2*k/n) * binomial(n,k) * a(n-k).

%F a(n) ~ sqrt(2*Pi) * n^(n + 1/10) / (6^(3/5) * Gamma(3/5) * exp(n) * log(6/5)^(n + 3/5)). - _Vaclav Kotesovec_, Nov 11 2023

%F a(0) = 1; a(n) = 3*a(n-1) - 6*Sum_{k=1..n-1} (-1)^k * binomial(n-1,k) * a(n-k). - _Seiichi Manyama_, Nov 16 2023

%t a[n_] := Sum[Product[5*j + 3, {j, 0, k - 1}] * StirlingS2[n, k], {k, 0, n}]; Array[a, 18, 0] (* _Amiram Eldar_, Sep 11 2023 *)

%o (PARI) a(n) = sum(k=0, n, prod(j=0, k-1, 5*j+3)*stirling(n, k, 2));

%Y Cf. A094418, A346984, A365568, A365570.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Sep 09 2023

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 12 11:18 EDT 2024. Contains 373331 sequences. (Running on oeis4.)