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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.)