A047794 a(n) = Sum_{k=0..n} C(n,k)*|Stirling1(n,k)*Stirling2(n,k)|.

1, 1, 3, 34, 631, 16871, 617356, 28968990, 1680536159, 117572734195, 9715771690081, 932711356031016, 102653506699902874, 12810868034079756421, 1795954763065584594656, 280569433733767673934426, 48506369621902094002862671, 9224242346164172284054561019

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..275

Maple

seq(add((-1)^(n-k)*binomial(n, k)*stirling1(n, k)*stirling2(n, k), k = 0 .. n), n = 0..20); # G. C. Greubel, Aug 07 2019

Mathematica

Table[Sum[Binomial[n, k]Abs[StirlingS1[n, k]StirlingS2[n, k]], {k, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Apr 10 2012 *)

Prog

(PARI) {a(n) = sum(k=0, n, (-1)^(n-k)*stirling(n, k, 1)*stirling(n, k, 2) *binomial(n, k))};
vector(20, n, n--; a(n)) \\ G. C. Greubel, Aug 07 2019
(Magma) [(&+[(-1)^(n-k)*StirlingFirst(n, k)*StirlingSecond(n, k) *Binomial(n, k): k in [0..n]]): n in [0..20]]; // G. C. Greubel, Aug 07 2019
(Sage) [sum(stirling_number1(n, k)*stirling_number2(n, k)*binomial(n, k) for k in (0..n)) for n in (0..20)] # G. C. Greubel, Aug 07 2019
(GAP) List([0..20], n-> Sum([0..n], k-> Stirling1(n, k)*Stirling2(n, k) *Binomial(n, k) )); # G. C. Greubel, Aug 07 2019

Crossrefs

Cf. A008275, A008277, A047792, A047793, A047795.

Sequence in context: A262673 A365040 A126753 * A332679 A256512 A277391

Adjacent sequences: A047791 A047792 A047793 * A047795 A047796 A047797

Keyword

nonn

Author

N. J. A. Sloane

Status

approved