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!)
A187056 G.f.: A(x,y,z) = Sum_{n>=0} ((2n)!/n!^2)*[Sum_{k=0..2n} T(n,k)*z^k]*x^(2n)*y^n/(1-x-xy)^(4n+1) where A(x,y,x+xy) = Sum_{n>=0, k=0..n} C(n,k)^4*x^n*y^k at z = x+xy; this is the triangle of coefficients T(n,k), read by rows. 1
1, 7, 4, 1, 131, 176, 96, 16, 1, 3067, 6588, 5895, 2416, 477, 36, 1, 79459, 235456, 298816, 197824, 73120, 14656, 1504, 64, 1, 2181257, 8252300, 13668975, 12563200, 6966400, 2373504, 490700, 58400, 3675, 100, 1, 62165039, 286326288, 587324232, 692965040, 516541455, 252283968, 81432456, 17138304, 2276145, 179440, 7632, 144, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..48.

FORMULA

Row sums equal A000897(n) = (4n)!/((2n)!*n!^2).

Column 0 equals A099601(n) = quotient of de Bruijn sums S(4,n)/S(2,n).

EXAMPLE

G.f.: A(x,y,z) = 1/(1-x-x*y)

+ 2*(7 + 4*z + z^2)*x^2*y/(1-x-x*y)^5

+ 6*(131 + 176*z + 96*z^2 + 16*z^3 + z^4)*x^4*y^2/(1-x-x*y)^9

+ 20*(3067 + 6588*z + 5895*z^2 + 2416*z^3 + 477*z^4 + 36*z^5 + z^6)*x^6*y^3/(1-x-x*y)^13 +...

G.f. at z = x+xy yields: A(x,y,x+xy) = 1 + (1 + y)*x

+ (1 + 16*y + y^2)*x^2

+ (1 + 81*y + 81*y^2 + y^3)*x^3

+ (1 + 256*y + 1296*y^2 + 256*y^3 + y^4)*x^4

+ (1 + 625*y + 10000*y^2 + 10000*y^3 + 625*y^4 + y^5)*x^5 +...

which is a series involving binomial coefficients to the 4th power.

...

This triangle of coefficients T(n,k) of z^k, k=0..2n, begins:

[1];

[7, 4, 1];

[131, 176, 96, 16, 1];

[3067, 6588, 5895, 2416, 477, 36, 1];

[79459, 235456, 298816, 197824, 73120, 14656, 1504, 64, 1];

[2181257, 8252300, 13668975, 12563200, 6966400, 2373504, 490700, 58400, 3675, 100, 1];

[62165039, 286326288, 587324232, 692965040, 516541455, 252283968, 81432456, 17138304, 2276145, 179440, 7632, 144, 1];

[1818812387, 9876304172, 24205612067, 34939683632, 32837525567, 21029302364, 9356637759, 2899564224, 619135629, 88879924, 8237341, 461776, 14161, 196, 1];

[54257991011, 339398092544, 968547444480, 1655445817088, 1881608595776, 1496188189440, 853911382016, 353544477440, 106191762336, 22927328512, 3492995968, 364541184, 24932320, 1044736, 24192, 256, 1];

...

CROSSREFS

Cf. A000897, A099601.

Sequence in context: A011407 A021907 A168422 * A103240 A155531 A216261

Adjacent sequences:  A187053 A187054 A187055 * A187057 A187058 A187059

KEYWORD

nonn,tabf

AUTHOR

Paul D. Hanna, Mar 02 2011

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 September 23 19:48 EDT 2021. Contains 347617 sequences. (Running on oeis4.)