A077386 Sums of rows of triangle in A077385.

1, 4, 17, 106, 937, 10886, 156865, 2696338, 53808401, 1222222222, 31124909521, 878100801722, 27181099309561, 915824738370166, 33363344029017857, 1306644371887759906, 54743840860125227041, 2443077625590307888670, 115697055886568046147601

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..385

Formula

a(n) = {n^n + n^(n-1) -2}/(n-1), for n>1.

E.g.f.: 2*x*Ei(-W(-x)) - 2*x*Ei(x) + W(-x) + 2*exp(x) - 2, where Ei(x) is the exponential integral and W(x) is the Lambert W function. - G. C. Greubel, Sep 21 2022

Mathematica

Table[If[n==1, 1, (n^n +n^(n-1) -2)/(n-1)], {n, 30}] (* G. C. Greubel, Sep 21 2022 *)

Prog

(PARI) a(n) = sum(k=0, n-1, n^k) + sum(k=0, n-2, n^k); \\ Michel Marcus, Feb 03 2014
(Magma) [1] cat [(n^n +n^(n-1) -2)/(n-1): n in [2..30]]; // G. C. Greubel, Sep 21 2022
(SageMath)
def A077386(n): return 1 if (n==1) else (n^n +n^(n-1) -2)/(n-1)
[A077386(n) for n in (1..30)] # G. C. Greubel, Sep 21 2022

Crossrefs

Cf. A077385.

Sequence in context: A335626 A232211 A122940 * A209903 A330514 A330535

Adjacent sequences: A077383 A077384 A077385 * A077387 A077388 A077389

Keyword

nonn

Author

Amarnath Murthy, Nov 06 2002

Extensions

More terms from Michel Marcus, Feb 03 2014

Status

approved