Entringer Number

Author

Eric W. Weisstein
January 25, 2009

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegerSequences/EntringerNumber.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/EntringerNumber.html.

©2009 Wolfram Research, Inc. except for portions noted otherwise

Enumeration

e[0,0]:=1
e[n_,0]:=0
e[n_,k_]:=e[n,k]=e[n,k-1]+e[n-1,n-k]

ColumnForm[Table[e[n,k],{n,0,5},{k,0,n}],Center]

Flatten[%4]

E(n,n)

Series[Sec[x]+Tan[x],{x,0,10}]

Table[n!SeriesCoefficient[Sec[z]+Tan[z],{z,0,n}],{n,8}]

FullSimplify[SeriesCoefficient[Sec[z]+Tan[z],{z,0,n}],n>0]

FullSimplify[((I (((2 I))^n) (-1+(((-1))^n)) (-1+(2^(1+n))) BernoulliB[1+n])/(Gamma[2+n]))n!,Mod[n,2]==1&&n>0]

Table[If[Mod[n,2]==0,(I^n) EulerE[n],-(((((2 I))^(1+n)) (-1+(2^(1+n))) BernoulliB[1+n])/(1+n))],{n,10}]

FunctionExpand[-(((((2 I))^(1+n)) (-1+(2^(1+n))) BernoulliB[1+n])/(1+n)),n∈Integers&&Mod[n,2]==1&&n>0]