A137391 Triangle: let f(t) = 1 + t + t^2 and g(t) = t + t^2, expansion of p(t) = f(t)*exp(x*g(t)).

1, 1, 1, 2, 4, 1, 0, 12, 9, 1, 0, 24, 48, 16, 1, 0, 0, 180, 140, 25, 1, 0, 0, 360, 840, 330, 36, 1, 0, 0, 0, 3360, 2940, 672, 49, 1, 0, 0, 0, 6720, 18480, 8400, 1232, 64, 1, 0, 0, 0, 0, 75600, 75600, 20664, 2088, 81, 1, 0, 0, 0, 0, 151200, 483840, 252000, 45360, 3330

Offset

1,4

Links

Table of n, a(n) for n=1..64.

Example

{1},
{1, 1},
{2, 4, 1},
{0, 12, 9, 1},
{0, 24, 48, 16, 1},
{0, 0, 180, 140, 25, 1},
{0, 0, 360, 840, 330, 36, 1},
{0, 0, 0, 3360, 2940, 672, 49, 1},
{0, 0, 0, 6720, 18480, 8400, 1232, 64, 1},
{0, 0, 0, 0, 75600, 75600, 20664, 2088, 81, 1},
{0, 0, 0, 0, 151200, 483840, 252000, 45360, 3330, 100, 1}

Mathematica

f[t_] = 1 + t + t^2;
g[t_] = t + t^2;
p[t_] = f[t]*Exp[x*g[t]];
Table[ ExpandAll[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}];
a = Table[ CoefficientList[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}];
Flatten[a]

Crossrefs

Sequence in context: A378394 A094344 A211183 * A276207 A248672 A276631

Adjacent sequences: A137388 A137389 A137390 * A137392 A137393 A137394

Keyword

nonn,uned,tabl,less

Author

Roger L. Bagula and Gary W. Adamson, Apr 10 2008

Status

approved