A154867 - OEIS

The OEIS is supported by the many generous donors to the OEIS 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 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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)].

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 A256894 A372068

Adjacent sequences: A154864 A154865 A154866 * A154868 A154869 A154870

KEYWORD

nonn,uned,tabl

AUTHOR

Roger L. Bagula, Jan 16 2009

STATUS

approved