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A072338 EULER transform of A002620 (with the initial 0,0,1 omitted). 0
1, 2, 7, 18, 48, 114, 273, 614, 1370, 2952, 6275, 13034, 26725, 53854, 107238, 210670, 409446, 786936, 1498147, 2825084, 5282409, 9795620, 18027645, 32935112, 59760481, 107724038, 192984835, 343676216, 608589028, 1071869694, 1878068324, 3274291480, 5681336242 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..32.

N. J. A. Sloane, Transforms

FORMULA

a(n) ~ exp(2*sqrt(2)*Pi*n^(3/4) / (3*15^(1/4)) + 2*Zeta(3) * sqrt(15*n) / Pi^2 + (7*5^(1/4)*Pi / (8*sqrt(2)*3^(3/4)) - 30*sqrt(2) * 15^(1/4) * Zeta(3)^2 /Pi^5) * n^(1/4) + 1200*Zeta(3)^3/Pi^8 - 71*Zeta(3)/(16*Pi^2) + 1/12) * Pi^(1/12) / (4*A * 2^(5/12) * 15^(13/48) * n^(37/48)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, May 31 2019

MATHEMATICA

nmax = 40; CoefficientList[Series[Product[1/(1 - x^k)^Floor[(k + 2)^2/4], {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, May 31 2019 *)

CROSSREFS

Sequence in context: A174192 A247289 A161870 * A182197 A022726 A192873

Adjacent sequences:  A072335 A072336 A072337 * A072339 A072340 A072341

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jul 16 2002

STATUS

approved

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Last modified January 23 13:37 EST 2020. Contains 331171 sequences. (Running on oeis4.)