A047796 a(n) = Sum_{k=0..n} Stirling1(n,k)^2.

1, 1, 2, 14, 194, 4402, 147552, 6838764, 418389078, 32639603798, 3161107700156, 372023906062756, 52280302234036252, 8645773770675973804, 1661888635268695003484, 367390786215560629372920, 92552610850186107484661670, 26356304249588730696338349990

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Vincenzo Librandi and Vaclav Kotesovec, Table of n, a(n) for n = 0..250 (terms 0..41 from Vincenzo Librandi)

Crossrefs

Cf. A000275, A047797, A342111.

Programs

GAP

List([0..20], n-> Sum([0..n], k-> Stirling1(n,k)^2 )); # G. C. Greubel, Aug 07 2019

Magma

[(&+[StirlingFirst(n,k)^2: k in [0..n]]): n in [0..10]]; // G. C. Greubel, Aug 07 2019

Maple

seq(add(stirling1(n, k)^2, k = 0..n), n = 0..20); # G. C. Greubel, Aug 07 2019

Mathematica

Table[Sum[StirlingS1[n,k]^2,{k,0,n}],{n,0,20}] (* Emanuele Munarini, Jul 04 2011 *)

Maxima

makelist(sum(stirling1(n,k)^2,k,0,n),n,0,24); /* Emanuele Munarini, Jul 04 2011 */

PARI

a(n) = sum(k=0, n, stirling(n, k, 1)^2); \\ Michel Marcus, Mar 26 2016

Sage

[sum(stirling_number1(n,k)^2 for k in (0..n)) for n in (0..20)] # G. C. Greubel, Aug 07 2019