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A277372 a(n) = Sum_{k=1..n} binomial(n,n-k)*n^(n-k)*n!/(n-k)!. 5
0, 1, 10, 141, 2584, 58745, 1602576, 51165205, 1874935168, 77644293201, 3588075308800, 183111507687581, 10230243235200000, 621111794820235849, 40722033570202507264, 2867494972696071121125, 215840579093024990396416, 17294837586403146090259745, 1469799445329208661211021312 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..18.

FORMULA

a(n) = n!*LaguerreL(n, -n) - n^n.

a(n) = (-1)^n*KummerU(-n, 1, -n) - n^n.

a(n) = n^n*(hypergeom([-n, -n], [], 1/n) - 1) for n>=1.

a(n) ~ n^n * phi^(2*n+1) * exp(n/phi-n) / 5^(1/4), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Oct 12 2016

MAPLE

a := n -> add(binomial(n, n-k)*n^(n-k)*n!/(n-k)!, k=1..n):

seq(a(n), n=0..18);

# Alternatively:

A277372 := n -> n!*LaguerreL(n, -n) - n^n:

seq(simplify(A277372(n)), n=0..18);

PROG

(PARI) a(n) = sum(k=1, n, binomial(n, n-k)*n^(n-k)*n!/(n-k)!); \\ Michel Marcus, Oct 12 2016

CROSSREFS

Cf. A097662, A239768.

Cf. A002720, A087912, A277382.

Sequence in context: A093471 A324448 A277310 * A181162 A245988 A184710

Adjacent sequences:  A277369 A277370 A277371 * A277373 A277374 A277375

KEYWORD

nonn

AUTHOR

Peter Luschny, Oct 11 2016

STATUS

approved

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Last modified February 18 00:37 EST 2020. Contains 332006 sequences. (Running on oeis4.)