login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A146568 Coefficients of Pascal's triangle polynomial minus MacMahon polynomial A060187 with a power of x divided out: q(x,n)=2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; p(x,n)=((x+1)^n-q(x,n))/x. 0
4, 20, 20, 72, 224, 72, 232, 1672, 1672, 232, 716, 10528, 23528, 10528, 716, 2172, 60636, 259688, 259688, 60636, 2172, 6544, 331584, 2485232, 4674944, 2485232, 331584, 6544, 19664, 1756304, 21707888, 69413168, 69413168, 21707888, 1756304 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

Row sums starting with n=2 are:{4, 40, 368, 3808, 46016, 644992, 10321664, 185794048, 3715890176}.

First elements in each row are: 3^n - 2*n - 1 (A061981).

LINKS

Table of n, a(n) for n=2..36.

FORMULA

q(x,n)=2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; p(x,n)=((x+1)^n-q(x,n))/x; t(n,m)=Coefficients(p(x,n)) with n starting at 2.

EXAMPLE

Traingle starts:

{4},

{20, 20},

{72, 224, 72},

{232, 1672, 1672, 232},

{716, 10528, 23528, 10528, 716},

{2172, 60636, 259688, 259688, 60636, 2172},

{6544, 331584, 2485232, 4674944, 2485232, 331584, 6544},

{19664, 1756304, 21707888, 69413168, 69413168, 21707888, 1756304, 19664},

{59028, 9116096, 178300784, 906923072, 1527092216, 906923072, 178300784, 9116096, 59028}

MATHEMATICA

q[x_, n_] = 2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; p[x_, n_] = (q[x, n] - (x + 1)^n)/x; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 2, 10}]; Flatten[%]

CROSSREFS

Cf. A061981, A060187.

Sequence in context: A288319 A330317 A151727 * A087326 A273791 A065984

Adjacent sequences:  A146565 A146566 A146567 * A146569 A146570 A146571

KEYWORD

nonn,tabl,changed

AUTHOR

Roger L. Bagula, Nov 01 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 8 09:33 EST 2021. Contains 341948 sequences. (Running on oeis4.)