A094089 E.g.f.: exp(-1)*Sum((1+2*x)^binomial(n,2)/n!, n=0..infinity).

1, 1, 5, 53, 873, 20457, 634541, 24950557, 1203940177, 69583310545, 4726132141013, 371490917377285, 33369568795430841, 3389380003596443833, 385790631214713169789, 48829461608868817380845, 6826282320001018166712481, 1047822371119145840154900897

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..150

Maple

A:= proc(k) exp(-1) *add((1+2*x)^binomial(n, 2)/ n!, n=0..k) end:
a:= proc(n) Digits:= 10+3*n; round(coeftayl(A(3*n+5), x=0, n)*n!) end:
seq(a(n), n=0..25);  # Alois P. Heinz, Sep 29 2008

Mathematica

A[k_] := (1/E) Sum[(1 + 2x)^Binomial[n, 2]/n!, {n, 0, k}];
a[n_] := SeriesCoefficient[A[3n + 5], {x, 0, n}] n! // Round;
a /@ Range[0, 25] (* Jean-François Alcover, Nov 18 2020, after Alois P. Heinz *)

Crossrefs

Sequence in context: A090360 A367156 A123130 * A357343 A231866 A196659

Adjacent sequences: A094086 A094087 A094088 * A094090 A094091 A094092

Keyword

easy,nonn

Author

Vladeta Jovovic, May 01 2004

Extensions

More terms from Alois P. Heinz, Sep 29 2008

Status

approved