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A294500 Binomial transform of the number of planar partitions (A000219). 8
1, 2, 6, 19, 60, 185, 559, 1662, 4875, 14134, 40564, 115370, 325465, 911355, 2534595, 7004827, 19246626, 52596377, 143006632, 386984573, 1042537831, 2796803110, 7473161196, 19893461042, 52767059608, 139488323734, 367540167625, 965445514862, 2528516552660 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..2930

FORMULA

a(n) = Sum_{k=0..n} binomial(n,k) * A000219(k).

a(n) ~ exp(1/12 + 3 * Zeta(3)^(1/3) * n^(2/3) / 2^(4/3) + Zeta(3)^(2/3) * n^(1/3) / 2^(5/3) - Zeta(3)/12) * 2^(n + 7/18) * Zeta(3)^(7/36) / (A * sqrt(3*Pi) * n^(25/36)), where A is the Glaisher-Kinkelin constant A074962.

G.f.: (1/(1 - x))*exp(Sum_{k>=1} sigma_2(k)*x^k/(k*(1 - x)^k)). - Ilya Gutkovskiy, Aug 20 2018

MATHEMATICA

nmax = 40; s = CoefficientList[Series[Product[1/(1-x^k)^k, {k, 1, nmax}], {x, 0, nmax}], x]; Table[Sum[Binomial[n, k] * s[[k+1]], {k, 0, n}], {n, 0, nmax}]

CROSSREFS

Cf. A218481, A266232, A294501, A294502, A294504.

Sequence in context: A014346 A183188 A118364 * A208481 A052544 A204200

Adjacent sequences:  A294497 A294498 A294499 * A294501 A294502 A294503

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Nov 01 2017

STATUS

approved

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Last modified December 4 10:44 EST 2021. Contains 349486 sequences. (Running on oeis4.)