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 A323631 Stirling transform of Pell numbers (A000129). 0

%I

%S 0,1,3,12,57,305,1798,11531,79707,589426,4634471,38547861,337734048,

%T 3105588629,29877483743,299906019892,3133423928557,34002824654365,

%U 382507638525838,4452923233600903,53561431659306039,664728428775177890,8500763141347126563,111886109022440334593,1513989730079050155936

%N Stirling transform of Pell numbers (A000129).

%F E.g.f.: exp(exp(x) - 1)*sinh(sqrt(2)*(exp(x) - 1))/sqrt(2).

%F a(n) = Sum_{k=0..n} Stirling2(n,k)*A000129(k).

%F a(n) = Sum_{k=0..n} binomial(n,k)*A000110(n-k)*A264037(k).

%t FullSimplify[nmax = 24; CoefficientList[Series[Exp[Exp[x] - 1] Sinh[Sqrt[2] (Exp[x] - 1)]/Sqrt[2], {x, 0, nmax}], x] Range[0, nmax]!]

%t Table[Sum[StirlingS2[n, k] Fibonacci[k, 2], {k, 0, n}], {n, 0, 24}]

%t Table[Sum[Binomial[n, k] BellB[n - k] (BellB[k, Sqrt[2]] - BellB[k, -Sqrt[2]])/(2 Sqrt[2]), {k, 0, n}], {n, 0, 24}]

%Y Cf. A000110, A000129, A263575, A263576, A264037.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Jan 21 2019

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Last modified July 21 04:40 EDT 2019. Contains 325189 sequences. (Running on oeis4.)