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!)
 A292916 a(n) = n! * [x^n] exp(n*x)/(2 - exp(x)). 5
 1, 2, 11, 94, 1083, 15666, 272451, 5532206, 128409707, 3352959850, 97259891163, 3102552150006, 107936130271899, 4066743353318114, 164961642651034547, 7167348523420169278, 332081754670735087275, 16343667009638859878298, 851478575825591156040843, 46814697307371602567813126 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The n-th term of the n-th binomial transform of A000670. LINKS G. C. Greubel, Table of n, a(n) for n = 0..380 N. J. A. Sloane, Transforms FORMULA a(n) = A292915(n,n). a(n) ~ n! * 2^(n-1) / (log(2))^(n+1). - Vaclav Kotesovec, Sep 27 2017 a(n) = 2^n*A000670(n) - Sum_{k=0..n-1} 2^k*(n-1-k)^n. - Seiichi Manyama, Dec 25 2023 MAPLE b:= proc(n, k) option remember; k^n +add( binomial(n, j)*b(j, k), j=0..n-1) end: a:= n-> b(n\$2): seq(a(n), n=0..20); # Alois P. Heinz, Sep 27 2017 MATHEMATICA Table[n! SeriesCoefficient[Exp[n x]/(2 - Exp[x]), {x, 0, n}], {n, 0, 19}] Table[HurwitzLerchPhi[1/2, -n, n]/2, {n, 0, 19}] PROG (PARI) a000670(n) = sum(k=0, n, k!*stirling(n, k, 2)); a(n) = 2^n*a000670(n)-sum(k=0, n-1, 2^k*(n-1-k)^n); \\ Seiichi Manyama, Dec 25 2023 (Magma) R:=PowerSeriesRing(Rationals(), 50); A292916:= func< n | Coefficient(R!(Laplace( Exp(n*x)/(2-Exp(x)) )), n) >; [A292916(n): n in [0..30]]; // G. C. Greubel, Jun 12 2024 (SageMath) [factorial(n)*( exp(n*x)/(2-exp(x)) ).series(x, n+1).list()[n] for n in (0..30)] # G. C. Greubel, Jun 12 2024 CROSSREFS Main diagonal of A292915. Cf. A000670, A330603. Sequence in context: A083069 A158837 A236962 * A290586 A098621 A266834 Adjacent sequences: A292913 A292914 A292915 * A292917 A292918 A292919 KEYWORD nonn,changed AUTHOR Ilya Gutkovskiy, Sep 26 2017 STATUS approved

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 15 09:26 EDT 2024. Contains 373407 sequences. (Running on oeis4.)