A342110 a(n) = Sum_{k=0..n} Stirling2(n,k) * Stirling2(n,n-k).

1, 0, 1, 6, 61, 770, 12160, 228382, 4989621, 124262532, 3475892685, 107901412520, 3681266754660, 136918473752216, 5513911474915116, 239034083286873630, 11098790133822288645, 549539910028075555016, 28903562131933534643851, 1609321474965547356327246

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..350

Formula

a(n) ~ c * d^n * (n-1)!, where

d = A238258 = 3.0882773047417401791158400820254382768364448971420138767247...

c = 0.12826577250734152801558828593238744179869387423941684693208180123477...

Mathematica

Table[Sum[StirlingS2[n, k]*StirlingS2[n, n-k], {k, 0, n}], {n, 0, 20}]

Prog

(PARI) a(n) = sum(k=0, n, stirling(n, k, 2)*stirling(n, n-k, 2)); \\ Michel Marcus, Feb 28 2021
(Magma) [(&+[StirlingSecond(n, k)*StirlingSecond(n, n-k): k in [0..n]]): n in [0..30]]; // G. C. Greubel, Jun 03 2021
(Sage) [sum( stirling_number2(n, k)*stirling_number2(n, n-k) for k in (0..n) ) for n in (0..30)] # G. C. Greubel, Jun 03 2021

Crossrefs

Cf. A008277, A014322, A047797, A342111.

Cf. A048993.

Sequence in context: A034659 A369509 A064088 * A191803 A259271 A047737

Adjacent sequences: A342107 A342108 A342109 * A342111 A342112 A342113

Keyword

nonn

Author

Vaclav Kotesovec, Feb 28 2021

Status

approved