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 A307523 Expansion of e.g.f. Product_{k>=1} (1 + log(1 + x)^k)/(1 - log(1 + x)^k). 1
 1, 2, 6, 28, 124, 848, 5312, 40080, 367632, 3132096, 27731328, 474979008, 1130161728, 90279554688, 268809015168, 3005011325952, 473192066191104, -7913323872693504, 186235895195313408, 1357401816746159616, -181477915903332002304, 9552839425392612096000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Exponential convolution of A298905 and A306042. LINKS FORMULA E.g.f.: exp(Sum_{k>=1} (sigma(2*k) - sigma(k))*log(1 + x)^k/k). E.g.f.: 1/theta_4(log(1 + x)). a(n) = Sum_{k=0..n} Stirling1(n,k)*A015128(k)*k!. MATHEMATICA nmax = 21; CoefficientList[Series[Product[(1 + Log[1 + x]^k)/(1 - Log[1 + x]^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! nmax = 21; CoefficientList[Series[Exp[Sum[(DivisorSigma[1, 2 k] - DivisorSigma[1, k]) Log[1 + x]^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]! nmax = 21; CoefficientList[Series[1/EllipticTheta[4, 0, Log[1 + x]], {x, 0, nmax}], x] Range[0, nmax]! Table[Sum[StirlingS1[n, k] Sum[PartitionsQ[j] PartitionsP[k - j], {j, 0, k}] k!, {k, 0, n}], {n, 0, 21}] CROSSREFS Cf. A015128, A298905, A306042, A306045, A307524. Sequence in context: A047125 A189238 A226497 * A065577 A227294 A302336 Adjacent sequences:  A307520 A307521 A307522 * A307524 A307525 A307526 KEYWORD sign AUTHOR Ilya Gutkovskiy, Apr 12 2019 STATUS approved

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Last modified January 19 17:59 EST 2020. Contains 331051 sequences. (Running on oeis4.)