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A266083 a(n) = Sum_{k = 0..n - 1} (a(n - 1) + k) for n>0, a(0) = 1. 1
1, 1, 3, 12, 54, 280, 1695, 11886, 95116, 856080, 8560845, 94169350, 1130032266, 14690419536, 205665873595, 3084988104030, 49359809664600, 839116764298336, 15104101757370201, 286977933390033990, 5739558667800679990, 120530732023814280000, 2651676104523914160231 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..320

Eric Weisstein's World of Mathematics, Incomplete Gamma Function

FORMULA

a(n) = (2*n! + exp(1)*n*(n - 1)*Gamma(n - 1, 1))/2, where Gamma(a, x) is the incomplete gamma function.

a(n + 1) - a(n)*(n + 1) = A000217(n).

a(n) = n*a(n-1) + binomial(n,2). - G. C. Greubel, Dec 22 2015

EXAMPLE

a(0) = 1;

a(1) = 1 + 0 = 1;

a(2) = 1 + 0 + 1 + 1 = 3;

a(3) = 3 + 0 + 3 + 1 + 3 + 2 = 12;

a(4) = 12 + 0 + 12 + 1 + 12 + 2 + 12 + 3 = 54;

a(5) = 54 + 0 + 54 + 1 + 54 + 2 + 54 + 3 + 54 + 4 = 280, etc.

MATHEMATICA

Table[(2 n! + Exp[1] n (n - 1) Gamma[n - 1, 1])/2, {n, 0, 22}]

RecurrenceTable[{a[n] == n*a[n - 1] + Binomial[n, 2], a[0] == 1}, a, {n, 0, 20}] (* G. C. Greubel, Dec 22 2015 *)

PROG

(PARI) a(n) = (2*n! + exp(1)*n*(n-1)*incgam(n-1, 1))\/2

CROSSREFS

Cf. A000217, A038155 (for a(0) = 0).

Sequence in context: A270489 A335819 A263853 * A245374 A052673 A180589

Adjacent sequences:  A266080 A266081 A266082 * A266084 A266085 A266086

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 21 2015

STATUS

approved

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Last modified September 24 07:17 EDT 2021. Contains 347623 sequences. (Running on oeis4.)