The OEIS is supported by the many generous donors to the OEIS Foundation.

 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 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A278558 Expansion of Product_{n>=1} (1 - x^(5*n))^30/(1 - x^n)^31 in powers of x. 11
 1, 31, 527, 6448, 63240, 526443, 3852742, 25380847, 153068700, 855816380, 4479330091, 22117432019, 103672066076, 463698703204, 1987628351600, 8195086588810, 32603090921532, 125497791966435, 468512597653134, 1699911932127300, 6005651320362628, 20693956328627358 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS In general, if m>0 and g.f. = Product_{k>=1} (1 - x^(5*k))^m/(1 - x^k)^(m+1) then a(n) ~ sqrt(4*m+5) * exp(Pi*sqrt(2*(4*m+5)*n/15)) / (4*sqrt(3)*5^((m+1)/2)*n). - Vaclav Kotesovec, Nov 28 2016 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1000 FORMULA G.f.: Product_{n>=1} (1 - x^(5*n))^30/(1 - x^n)^31. A278559(n) = 5^2*63*A160460(n) + 5^5*52*A278555(n-1) + 5^7*63*A278556(n-2) + 5^10*6*A278557(n-3) + 5^12*a(n-4) for n >= 4. a(n) ~ exp(Pi*5*sqrt(2*n/3)) / (24414062500*sqrt(3)*n). - Vaclav Kotesovec, Nov 28 2016 MATHEMATICA nmax = 50; CoefficientList[Series[Product[(1 - x^(5*k))^30/(1 - x^k)^31, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 28 2016 *) CROSSREFS Cf. A160460, A278555, A278556, A278557, A278559. Sequence in context: A319427 A241888 A316457 * A022659 A038395 A261620 Adjacent sequences: A278555 A278556 A278557 * A278559 A278560 A278561 KEYWORD nonn AUTHOR Seiichi Manyama, Nov 23 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 7 11:41 EST 2023. Contains 367656 sequences. (Running on oeis4.)