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!)
A177447 G.f.: Sum_{n>=0} a(n)*x^n/(1+x)^(n^2) = 1+x. 10
1, 1, 1, 3, 18, 172, 2313, 40626, 887326, 23282964, 715540140, 25259729071, 1008721104654, 45008479039824, 2221170817590696, 120209722115431950, 7083266027910364710, 451620678137942740132, 30990400538494184551692, 2277988537997377457967690, 178626191260072536476398000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Column 1 of triangle A215241.

LINKS

Paul D. Hanna, Table of n, a(n) for n = 0..200

FORMULA

a(n) = number of subpartitions of the partition [0,0,2,6,12,...,(n-1)^2-(n-1)] for n>0 with a(0)=1. See A115728 for the definition of subpartitions.

EXAMPLE

1+x = 1 + 1*x/(1+x) + 1*x^2/(1+x)^4 + 3*x^3/(1+x)^9 + 18*x^4/(1+x)^16 + 172*x^5/(1+x)^25 + 2313*x^6/(1+x)^36 +...

Also forms the final terms in rows of the triangle where row n+1 equals the partial sums of row n with the final term repeated 2n+1 times, starting with a '1' in row 0, as illustrated by:

1;

1, 1,. 1;

1, 2,. 3,. 3,. 3,.. 3,.. 3;

1, 3,. 6,. 9, 12,. 15,. 18,. 18,. 18,. 18,. 18,. 18,. 18;

1, 4, 10, 19, 31,. 46,. 64,. 82, 100, 118, 136, 154, 172,. 172,. 172,. 172,. 172,. 172,. 172,. 172,. 172;

1, 5, 15, 34, 65, 111, 175, 257, 357, 475, 611, 765, 937, 1109, 1281, 1453, 1625, 1797, 1969, 2141, 2313, 2313, 2313, 2313, 2313, 2313, 2313, 2313, 2313; ...

PROG

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

(PARI) {A=[1, 1]; for(i=1, 40, A=concat(A, -Vec(sum(n=0, #A-1, A[n+1]*x^n/(1+x+x*O(x^#A))^(n^2)))[#A+1])); for(n=0, #A-1, print1(A[n+1], ", "))}

CROSSREFS

Cf. A215241, A215242, A215243, A133316, A177448, A177449, A177450.

Sequence in context: A289683 A193098 A322771 * A328031 A005192 A080687

Adjacent sequences:  A177444 A177445 A177446 * A177448 A177449 A177450

KEYWORD

nonn

AUTHOR

Paul D. Hanna, May 09 2010

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 October 21 22:47 EDT 2021. Contains 348160 sequences. (Running on oeis4.)