login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A294841 Expansion of Product_{k>=1} (1 + x^(2*k-1))^(k*(3*k-2))*(1 + x^(2*k))^(k*(3*k+2)). 3
1, 1, 5, 13, 34, 87, 212, 504, 1167, 2665, 5933, 13042, 28191, 60148, 126688, 263821, 543414, 1108272, 2239182, 4484482, 8907530, 17555485, 34345465, 66724969, 128772908, 246951514, 470738283, 892159198, 1681544803, 3152656375, 5880839454, 10916463171, 20169007200, 37095527149 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Weigh transform of the generalized octagonal numbers (A001082).

LINKS

Table of n, a(n) for n=0..33.

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Octagonal Number

FORMULA

G.f.: Product_{k>=1} (1 + x^k)^A001082(k+1).

a(n) ~ exp(Pi/3 * (7/5)^(1/4) * 2^(3/4) * n^(3/4) + 9*Zeta(3) / (2*Pi^2) * sqrt(5*n/14) - (405*Zeta(3)^2 / (56*Pi^5) + Pi/48) * (10*n/7)^(1/4) + (6075*Zeta(3)^2 / (196*Pi^8) + 15/(224*Pi^2)) * Zeta(3)) * 7^(1/8) / (2^(9/4) * 5^(1/8) * n^(5/8)). - Vaclav Kotesovec, Nov 10 2017

MATHEMATICA

nmax = 33; CoefficientList[Series[Product[(1 + x^(2 k - 1))^(k (3 k - 2)) (1 + x^(2 k))^(k (3 k + 2)), {k, 1, nmax}], {x, 0, nmax}], x]

a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(k/d + 1) d (d^2 + d - Ceiling[d/2]^2), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 33}]

CROSSREFS

Cf. A001082, A028377, A294838, A294839, A294840.

Sequence in context: A106587 A034509 A034521 * A092647 A171262 A006561

Adjacent sequences:  A294838 A294839 A294840 * A294842 A294843 A294844

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Nov 09 2017

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 November 30 11:07 EST 2021. Contains 349419 sequences. (Running on oeis4.)