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 A320566 Expansion of e.g.f. exp(x) * Product_{k>=1} 1/(1 - x^k/k!). 6
 1, 2, 6, 23, 110, 617, 4035, 29927, 249926, 2316317, 23674841, 264329177, 3207278255, 42011308653, 591460307157, 8905905152798, 142897741683846, 2433947385964373, 43873382718719949, 834402502632550589, 16699964488044322205, 350869837371828862607, 7721899536993122262447 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A005651. LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..440 N. J. A. Sloane, Transforms FORMULA E.g.f.: exp(x + Sum_{k>=1} Sum_{j>=1} x^(j*k)/(k*(j!)^k)). a(n) = Sum_{k=0..n} binomial(n,k)*A005651(k). a(n) ~ exp(1) * A247551 * n!. - Vaclav Kotesovec, Jul 21 2019 MAPLE seq(coeff(series(factorial(n)*exp(x)*mul((1-x^k/factorial(k))^(-1), k=1..n), x, n+1), x, n), n = 0 .. 22); # Muniru A Asiru, Oct 15 2018 MATHEMATICA nmax = 22; CoefficientList[Series[Exp[x] Product[1/(1 - x^k/k!), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! nmax = 22; CoefficientList[Series[Exp[x + Sum[Sum[x^(j k)/(k (j!)^k), {j, 1, nmax}], {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]! Table[Sum[Binomial[n, k] Total[Apply[Multinomial, IntegerPartitions[k], {1}]], {k, 0, n}], {n, 0, 22}] CROSSREFS Cf. A005651, A320567, A327870. Row sums of A327801. Sequence in context: A208733 A264899 A224786 * A205802 A117226 A117156 Adjacent sequences:  A320563 A320564 A320565 * A320567 A320568 A320569 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Oct 15 2018 STATUS approved

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Last modified May 11 19:29 EDT 2021. Contains 343808 sequences. (Running on oeis4.)