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!)
A305842 Product_{n>=1} (1 + x^n)^a(n) = g.f. of A000293 (solid partitions). 0
1, 4, 6, 14, 15, 26, 26, 48, 46, 83, 97, 146, 112, 49, -186, -448, -735, -485, 779, 3977, 9323, 16569, 23056, 23996, 10116, -31501, -120720, -283153, -548924, -932348, -1380125, -1655520, -1144651, 1384894, 7943203, 21083482, 42787785, 71816970, 98995196 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Inverse weigh transform of A000293.

LINKS

Table of n, a(n) for n=1..39.

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Solid Partition

FORMULA

Product_{n>=1} (1 + x^n)^a(n) = Sum_{k>=0} A000293(k)*x^k.

EXAMPLE

(1 + x) * (1 + x^2)^4 * (1 + x^3)^6 * (1 + x^4)^14 * (1 + x^5)^15 * ... * (1 + x^n)^a(n) * ... = 1 + x + 4*x^2 + 10*x^3 + 26*x^4 + 59*x^5 + ... + A000293(k)*x^k + ...

CROSSREFS

Cf. A000293, A001511, A037452, A193718, A305841.

Sequence in context: A310615 A310616 A310617 * A094298 A089226 A102029

Adjacent sequences:  A305839 A305840 A305841 * A305843 A305844 A305845

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Jun 11 2018

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 February 17 23:35 EST 2020. Contains 332006 sequences. (Running on oeis4.)