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!)
A209196 Triangle defined by g.f. A(x,y) = exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n^2, n*k) * y^k ), as read by rows. 8
1, 1, 1, 1, 4, 1, 1, 32, 32, 1, 1, 487, 3282, 487, 1, 1, 11113, 657573, 657573, 11113, 1, 1, 335745, 209282906, 1513844855, 209282906, 335745, 1, 1, 12607257, 96673776804, 5580284351032, 5580284351032, 96673776804, 12607257, 1, 1, 565877928, 61162554558200 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Paul D. Hanna, Rows n = 0..30, flattened.

FORMULA

Column 1 equals A209197.

Row sums equal A167006.

Antidiagonal sums equal A206830.

EXAMPLE

This triangle begins:

1;

1, 1;

1, 4, 1;

1, 32, 32, 1;

1, 487, 3282, 487, 1;

1, 11113, 657573, 657573, 11113, 1;

1, 335745, 209282906, 1513844855, 209282906, 335745, 1;

1, 12607257, 96673776804, 5580284351032, 5580284351032, 96673776804, 12607257, 1;

1, 565877928, 61162554558200, 31336815578461815, 229089181252258800, 31336815578461815, 61162554558200, 565877928, 1; ...

G.f.: A(x,y) = 1 + (1+y)*x + (1+4*y+y^2)*x^2 + (1+32*y+32*y^2+y^3)*x^3 + (1+487*y+3282*y^2+487*y^3+y^4)*x^4 +...

The logarithm of the g.f. equals the series:

log(A(x,y)) = (1 + y)*x

+ (1 + 6*y + y^2)*x^2/2

+ (1 + 84*y + 84*y^2 + y^3)*x^3/3

+ (1 + 1820*y + 12870*y^2 + 1820*y^3 + y^4)*x^4/4

+ (1 + 53130*y + 3268760*y^2 + 3268760*y^3 + 53130*y^4 + y^5)*x^5/5 +...

in which the coefficients form A209330(n,k) = binomial(n^2, n*k).

PROG

(PARI) {T(n, k)=polcoeff(polcoeff(exp(sum(m=1, n, x^m/m*sum(j=0, m, binomial(m^2, m*j)*y^j))+x*O(x^n)), n, x), k, y)}

for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print(""))

CROSSREFS

Cf. A209197, A167006, A206830, A209330 (log), A155200.

Sequence in context: A173918 A174412 A177939 * A158390 A228836 A176419

Adjacent sequences:  A209193 A209194 A209195 * A209197 A209198 A209199

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Mar 05 2012

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 22 03:21 EDT 2020. Contains 337289 sequences. (Running on oeis4.)