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A285240 Expansion of Product_{k>=1} (1 + k*x^k)^(k^2). 3
1, 1, 8, 35, 115, 429, 1425, 4803, 15398, 48940, 151046, 459000, 1373219, 4037721, 11723911, 33566828, 94993571, 265722551, 735543433, 2015558930, 5471271099, 14719853084, 39266487114, 103908002173, 272855152096, 711272144097, 1841162650896, 4734074846631 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..5000

MATHEMATICA

nmax = 40; CoefficientList[Series[Product[(1 + k*x^k)^(k^2), {k, 1, nmax}], {x, 0, nmax}], x]

nmax = 40; s = 1 + x; Do[s*=Sum[Binomial[k^2, j]*k^j*x^(j*k), {j, 0, Floor[nmax/k] + 1}]; s = Select[Expand[s], Exponent[#, x] <= nmax &]; , {k, 2, nmax}]; CoefficientList[s, x]

CROSSREFS

Cf. A022629, A027998, A266891, A285241, A285242.

Sequence in context: A267170 A266762 A220889 * A036598 A229403 A059824

Adjacent sequences:  A285237 A285238 A285239 * A285241 A285242 A285243

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Apr 15 2017

STATUS

approved

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Last modified July 22 14:46 EDT 2019. Contains 325224 sequences. (Running on oeis4.)