A178603 Triangle T(n,k): the coefficient of [t^n] [x^k] of 2^(n+5) *n! *exp(t*(1+t)*x) / (3+exp(t*(1+t))).

8, -4, 16, -20, 48, 32, -46, -216, 336, 64, -124, -1328, 288, 1408, 128, 1306, -4920, -15280, 9920, 4800, 256, 17726, 792, -109200, -49600, 72000, 14592, 512, 164321, 467572, -407736, -1365280, 243040, 362880, 41216, 1024, 627364, 6599760

Offset

0,1

Comments

Row sums are 8, 12, 60, 138, 372, -3918, -53178, -492963, -1882092, 33032874, 953238882, ....

Links

Table of n, a(n) for n=0..37.

Example

8;
-4, 16;
-20, 48, 32;
-46, -216, 336, 64;
-124, -1328, 288, 1408, 128;
1306, -4920, -15280, 9920, 4800, 256;
17726, 792, -109200, -49600, 72000, 14592, 512;
164321, 467572, -407736, -1365280, 243040, 362880, 41216, 1024;
627364, 6599760, 3829280, -10328192, -8238720, 4003328, 1512448, 110592, 2048;
-11010958, 58617000, 126728208, -16166976, -144777024, -15660288, 29428224, 5584896, 285696, 4096;

Maple

A178603 := proc(n, k)
    2^(n+5)*n!*exp(t*(1+t)*x)/(3+exp(t*(1+t))) ;
    coeftayl(%, t=0, n) ;
    coeftayl(%, x=0, k) ;
end proc: # R. J. Mathar, Jun 16 2015

Mathematica

p[t_] = 4*Exp[(t + t^2)*x] /(3 + Exp[t + t^2]);
a = Table[ CoefficientList[FullSimplify[ExpandAll[2^(n + 3)*n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]]], x], {n, 0, 10}];
Flatten[a]

Prog

(PARI) T(n, k)=my(t='t, x='x); polcoeff(polcoeff(2^(n+5)*n!*exp(t*(1+t)*x)/(3+exp(t*(1+t))), k, x), n, t) \\ Charles R Greathouse IV, Jun 16 2015

Crossrefs

Sequence in context: A220130 A276071 A040059 * A018810 A070485 A248293

Adjacent sequences: A178600 A178601 A178602 * A178604 A178605 A178606

Keyword

sign,tabl,less

Author

Roger L. Bagula, May 30 2010

Status

approved