A047797 a(n) = Sum_{k=0..n} Stirling2(n,k)^2.

1, 1, 2, 11, 87, 952, 13513, 237113, 5016728, 125121009, 3615047527, 119384499720, 4455637803543, 186152008588691, 8636436319397292, 441871067839416319, 24781002306869712365, 1515279889256750470086, 100546673139756241189021

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

If S is the lower matrix of Stirling numbers of the second kind, this sequence (without the first term 1) is the diagonal of the matrix S.Transpose[S]. - Sergio Falcon, May 02 2007

Links

• G. C. Greubel, Table of n, a(n) for n = 0..320

Crossrefs

Cf. A008277, A047796, A342110.

Programs

GAP

List([0..20], n-> Sum([0..n], k-> Stirling2(n,k)^2 )); # G. C. Greubel, Aug 07 2019

Magma

[(&+[StirlingSecond(n,k)^2: k in [0..n]]): n in [0..20]]; // G. C. Greubel, Aug 07 2019

Maple

seq(add(Stirling2(n, k)^2, k = 0..n), n = 0..20); # G. C. Greubel, Aug 07 2019

Mathematica

Table[Sum[StirlingS2[n,k]^2,{k,0,n}],{n,0,20}] (* Emanuele Munarini, Jul 01 2011 *)

Maxima

makelist(sum(stirling2(n,k)^2,k,0,n),n,0,20); /* Emanuele Munarini, Jul 01 2011 */

PARI

{a(n) = sum(k=0,n, stirling(n,k,2)^2)};
vector(20, n, n--; a(n)) \\ G. C. Greubel, Aug 07 2019

Sage

[sum(stirling_number2(n,k)^2 for k in (0..n)) for n in (0..20)] # G. C. Greubel, Aug 07 2019