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A323631 Stirling transform of Pell numbers (A000129). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
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).
MAPLE
b:= proc(n, m) option remember; `if`(n=0,
(<<2|1>, <1|0>>^m)[1, 2], m*b(n-1, m)+b(n-1, m+1))
end:
a:= n-> b(n, 0):
seq(a(n), n=0..24); # Alois P. Heinz, Jun 23 2023
MATHEMATICA
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}]
CROSSREFS
Sequence in context: A117107 A159609 A128326 * A014333 A185618 A027710
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 21 2019
STATUS
approved

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Last modified June 23 17:30 EDT 2024. Contains 373653 sequences. (Running on oeis4.)