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A154867 A triangular sequence of polynomial coefficients: p(x,n) = Sum[m^n*x^m/m!, {m, 0, Infinity}]/(x*Exp[x]); q(x,n)= If[n == 0, 1, p(x, n) + x^n*p(1/x, n)]. 0
1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 8, 12, 8, 1, 1, 16, 35, 35, 16, 1, 1, 32, 105, 130, 105, 32, 1, 1, 64, 322, 490, 490, 322, 64, 1, 1, 128, 994, 1967, 2100, 1967, 994, 128, 1, 1, 256, 3061, 8232, 9597, 9597, 8232, 3061, 256, 1, 1, 512, 9375, 34855, 48405, 45654, 48405 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 4, 10, 30, 104, 406, 1754, 8280, 42294, 231950,...}

LINKS

Table of n, a(n) for n=0..61.

FORMULA

p(x,n) = Sum[m^n*x^m/m!, {m, 0, Infinity}]/(x*Exp[x]);

q(x,n)= If[n == 0, 1, p(x, n) + x^n*p(1/x, n)];

t(n,m)=coefficients(q(x,n)).

EXAMPLE

{1},

{1, 1},

{1, 2, 1},

{1, 4, 4, 1},

{1, 8, 12, 8, 1},

{1, 16, 35, 35, 16, 1},

{1, 32, 105, 130, 105, 32, 1},

{1, 64, 322, 490, 490, 322, 64, 1},

{1, 128, 994, 1967, 2100, 1967, 994, 128, 1},

{1, 256, 3061, 8232, 9597, 9597, 8232, 3061, 256, 1},

{1, 512, 9375, 34855, 48405, 45654, 48405, 34855, 9375, 512, 1}

MATHEMATICA

Clear[p]; p[x_, n_] = Sum[m^n*x^m/m!, {m, 0, Infinity}]/(x*Exp[x]);

q[x_, n_] = If[n == 0, 1, p[x, n] + x^n*p[1/x, n]];

Table[FullSimplify[ExpandAll[q[x, n]]], {n, 0, 10}];

Table[CoefficientList[FullSimplify[ExpandAll[q[x, n]]], x], {n, 0, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A137854 A062715 A100631 * A064298 A099594 A117401

Adjacent sequences:  A154864 A154865 A154866 * A154868 A154869 A154870

KEYWORD

nonn,uned,tabl

AUTHOR

Roger L. Bagula, Jan 16 2009

STATUS

approved

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Last modified November 23 12:14 EST 2014. Contains 249842 sequences.