A047793 a(n) = Sum_{k=0..n} |Stirling1(n,k)*Stirling2(n,k)|.

1, 1, 2, 12, 120, 1750, 34615, 882868, 28008694, 1076404824, 49100939538, 2615329877358, 160486317081673, 11218516998346216, 884855465842682269, 78106000651400369100, 7660758993518625156050, 829683453926089044978468

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..290

Maple

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

Mathematica

Table[Sum[Abs[StirlingS1[n, k]StirlingS2[n, k]], {k, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Jul 18 2017 *)

Prog

(Maxima) makelist(sum(abs(stirling1(n, k))*stirling2(n, k), k, 0, n), n, 0, 12); /* Emanuele Munarini, Jul 01 2011 */
(PARI) {a(n) = sum(k=0, n, (-1)^(n-k)*stirling(n, k, 1)*stirling(n, k, 2))};
vector(20, n, n--; a(n)) \\ G. C. Greubel, Aug 07 2019
(Magma) [(&+[(-1)^(n-k)*StirlingFirst(n, k)*StirlingSecond(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) 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) )); # G. C. Greubel, Aug 07 2019

Crossrefs

Cf. A008275, A008277, A047792, A047794, A047795.

Sequence in context: A303557 A131815 A177774 * A048800 A251185 A052738

Adjacent sequences: A047790 A047791 A047792 * A047794 A047795 A047796

Keyword

nonn

Author

N. J. A. Sloane

Status

approved