A323631 Stirling transform of Pell numbers (A000129).

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

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..553

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

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

Sequence in context: A117107 A159609 A128326 * A014333 A185618 A027710

Adjacent sequences: A323628 A323629 A323630 * A323632 A323633 A323634

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 21 2019

Status

approved