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!)
A196010 a(n) = [x^(n*(n+1)/2)] G(x)^n where G(x) = Sum_{n>=0} x^(n*(n+1)/2)). 9
1, 1, 2, 6, 32, 126, 842, 6594, 50654, 437802, 3962082, 38901699, 398593494, 4291288911, 48518097812, 571756012282, 7011537065184, 89099102516820, 1171925227051470, 15914369767022370, 222668594799098538, 3205203680348068734, 47392228013770511784 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of ordered ways of writing n-th triangular number as a sum of n triangular numbers (with 0's allowed). - Ilya Gutkovskiy, Jan 27 2018

LINKS

Paul D. Hanna, Table of n, a(n) for n = 0..100

EXAMPLE

Let G(x) = 1 + x + x^3 + x^6 + x^10 + x^15 + x^21 + x^28 + x^36 +...

then a(n) = the coefficient of x^(n*(n+1)/2) in G(x)^n.

Coefficients in powers of G(x) begin:

n=0: [(1),0,0,0,0,0,0,0,...];

n=1: [1,(1),0,1,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,...];

n=2: [1,2,1,(2),2,0,3,2,0,2,2,2,1,2,0,2,4,0,2,0,1,4,2,0,2,2,0,2,2,...];

n=3: [1,3,3,4,6,3,(6),9,3,7,9,6,9,9,6,6,15,9,7,12,3,15,15,6,12,12,...];

n=4: [1,4,6,8,13,12,14,24,18,20,(32),24,31,40,30,32,48,48,38,56,42,...];

n=5: [1,5,10,15,25,31,35,55,60,60,90,90,95,135,125,(126),170,180,...];

n=6: [1,6,15,26,45,66,82,120,156,170,231,276,290,390,435,438,561,630, 651,780,861,(842),...]; ...

the coefficients in parenthesis form the initial terms of this sequence.

PROG

(PARI) {a(n)=local(G=sum(m=0, n, x^(m*(m+1)/2))+x*O(x^(n*(n+1)/2))); polcoeff(G^n, n*(n+1)/2)}

CROSSREFS

Cf. A000217, A232108.

Sequence in context: A212762 A108327 A188573 * A121071 A092199 A108485

Adjacent sequences:  A196007 A196008 A196009 * A196011 A196012 A196013

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 26 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 July 4 15:43 EDT 2020. Contains 335448 sequences. (Running on oeis4.)