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

0,3

Links

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

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 *)

Prog

(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
(Magma) [(&+[StirlingFirst(n, k)^2: k in [0..n]]): n in [0..10]]; // G. C. Greubel, Aug 07 2019
(Sage) [sum(stirling_number1(n, k)^2 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)^2 )); # G. C. Greubel, Aug 07 2019

Crossrefs

Cf. A000275, A047797, A342111.

Sequence in context: A067902 A132611 A156327 * A305112 A336949 A232686

Adjacent sequences: A047793 A047794 A047795 * A047797 A047798 A047799

Keyword

nonn

Author

N. J. A. Sloane

Status

approved