A261643 a(n) = Sum_{k=1..n} (k^2 + k)^(n-k).

1, 3, 11, 57, 397, 3487, 37519, 484437, 7353473, 129104523, 2589967603, 58757627185, 1493762354293, 42223299711159, 1318186323111959, 45185985199663629, 1691822823829309801, 68865092213424362659, 3034735030143197197435, 144238580771432519823465, 7368717925255301486594525

Offset: 1

Author

Paul D. Hanna, Aug 27 2015

Keywords

• nonn

Comments

Row sums of triangle A261642.

Examples

			Initial terms begin:
a(1) = 2^0 = 1;
a(2) = 2^1 + 6^0 = 3;
a(3) = 2^2 + 6^1 + 12^0 = 11;
a(4) = 2^3 + 6^2 + 12^1 + 20^0 = 57;
a(5) = 2^4 + 6^3 + 12^2 + 20^1 + 30^0 = 397;
a(6) = 2^5 + 6^4 + 12^3 + 20^2 + 30^1 + 42^0 = 3487; ...
		

Crossrefs

Cf. A261642.

Programs

Mathematica

Table[Sum[(k^2+k)^(n-k),{k,n}],{n,30}] (* Harvey P. Dale, Aug 23 2021 *)

PARI

{a(n) = sum(k=1,n, (k + k^2)^(n-k))}
for(n=1,30,print1(a(n),", "))

Formula

a(n)^(1/n) ~ n^2/(exp(2)*LambertW(n)^2). - Vaclav Kotesovec, Aug 28 2015