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A323631
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Stirling transform of Pell numbers (A000129).
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0
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0, 1, 3, 12, 57, 305, 1798, 11531, 79707, 589426, 4634471, 38547861, 337734048, 3105588629, 29877483743, 299906019892, 3133423928557, 34002824654365, 382507638525838, 4452923233600903, 53561431659306039, 664728428775177890, 8500763141347126563, 111886109022440334593, 1513989730079050155936
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..24.
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FORMULA
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E.g.f.: exp(exp(x) - 1)*sinh(sqrt(2)*(exp(x) - 1))/sqrt(2).
a(n) = Sum_{k=0..n} Stirling2(n,k)*A000129(k).
a(n) = Sum_{k=0..n} binomial(n,k)*A000110(n-k)*A264037(k).
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MATHEMATICA
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FullSimplify[nmax = 24; CoefficientList[Series[Exp[Exp[x] - 1] Sinh[Sqrt[2] (Exp[x] - 1)]/Sqrt[2], {x, 0, nmax}], x] Range[0, nmax]!]
Table[Sum[StirlingS2[n, k] Fibonacci[k, 2], {k, 0, n}], {n, 0, 24}]
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}]
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CROSSREFS
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Cf. A000110, A000129, A263575, A263576, A264037.
Sequence in context: A117107 A159609 A128326 * A014333 A185618 A027710
Adjacent sequences: A323628 A323629 A323630 * A323632 A323633 A323634
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, Jan 21 2019
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STATUS
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approved
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