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A294529
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Binomial transform of A001156.
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4
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1, 2, 4, 8, 17, 38, 86, 192, 420, 905, 1939, 4163, 8987, 19494, 42368, 91990, 199127, 429345, 921982, 1972553, 4206909, 8949412, 19001874, 40293048, 85373962, 180826115, 382957231, 811027414, 1717497958, 3636335170, 7695599294, 16275268520, 34389570596
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OFFSET
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0,2
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LINKS
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Vaclav Kotesovec, Table of n, a(n) for n = 0..3000
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FORMULA
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a(n) = Sum_{k=0..n} binomial(n,k) * A001156(k).
a(n) ~ exp(3 * 2^(-5/3) * Pi^(1/3) * Zeta(3/2)^(2/3) * n^(1/3)) * Zeta(3/2)^(2/3) * 2^(n - 7/6) / (sqrt(3) * Pi^(7/6) * n^(7/6)).
G.f.: (1/(1 - x))*Product_{k>=1} 1/(1 - x^(k^2)/(1 - x)^(k^2)). - Ilya Gutkovskiy, Aug 20 2018
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MATHEMATICA
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nmax = 40; s = CoefficientList[Series[Product[1/(1 - x^(k^2)), {k, 1, nmax}], {x, 0, nmax}], x]; Table[Sum[Binomial[n, k] * s[[k+1]], {k, 0, n}], {n, 0, nmax}]
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CROSSREFS
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Cf. A001156, A218481, A266232, A294500, A294530.
Sequence in context: A036374 A214999 A084635 * A154222 A114199 A006196
Adjacent sequences: A294526 A294527 A294528 * A294530 A294531 A294532
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KEYWORD
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nonn
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AUTHOR
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Vaclav Kotesovec, Nov 02 2017
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STATUS
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approved
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