The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A094089 E.g.f.: exp(-1)*Sum((1+2*x)^binomial(n,2)/n!, n=0..infinity). 1

%I

%S 1,1,5,53,873,20457,634541,24950557,1203940177,69583310545,

%T 4726132141013,371490917377285,33369568795430841,3389380003596443833,

%U 385790631214713169789,48829461608868817380845,6826282320001018166712481,1047822371119145840154900897

%N E.g.f.: exp(-1)*Sum((1+2*x)^binomial(n,2)/n!, n=0..infinity).

%H Alois P. Heinz, <a href="/A094089/b094089.txt">Table of n, a(n) for n = 0..150</a>

%p A:= proc(k) exp(-1) *add((1+2*x)^binomial(n,2)/ n!, n=0..k) end:

%p a:= proc(n) Digits:= 10+3*n; round(coeftayl(A(3*n+5), x=0, n)*n!) end:

%p seq(a(n), n=0..25); # _Alois P. Heinz_, Sep 29 2008

%t A[k_] := (1/E) Sum[(1 + 2x)^Binomial[n, 2]/n!, {n, 0, k}];

%t a[n_] := SeriesCoefficient[A[3n + 5], {x, 0, n}] n! // Round;

%t a /@ Range[0, 25] (* _Jean-François Alcover_, Nov 18 2020, after _Alois P. Heinz_ *)

%K easy,nonn

%O 0,3

%A _Vladeta Jovovic_, May 01 2004

%E More terms from _Alois P. Heinz_, Sep 29 2008

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

Last modified December 3 12:16 EST 2021. Contains 349462 sequences. (Running on oeis4.)