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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

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