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A185895 Exponential generating function is (1-x^1/1!)(1-x^2/2!)(1-x^3/3!).... 3
1, -1, -1, 2, 3, 14, -40, -43, -357, -1762, 8004, 13067, 78540, 492439, 3932305, -26867293, -44643557, -363632466, -1729625764, -15939972937, -145669871232, 1488599170613, 3515325612655, 26765194180353, 151925998229148 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..300

FORMULA

E.g.f.: Product_{k>0} (1 - x^k/k!).

a(n) = Sum_{k=1..n} (n-1)!/(n-k)!*b(k)*a(n-k), where b(k) = Sum_{d divides k} -d*d!^(-k/d) and a(0) = 1 [cf. Vladeta Jovovic's formula in A007837].

E.g.f.: exp(-Sum_{k>=1} Sum_{j>=1} x^(j*k)/(k*(j!)^k)). - Ilya Gutkovskiy, Jun 18 2018

PROG

(PARI) {a(n) = if( n<0, 0, n! * polcoeff( prod( k=1, n, 1 - x^k / k!, 1 + x * O(x^n)), n))}

(PARI) {a(n)=if(n<0, 0, if(n==0, 1, sum(k=1, n, (n-1)!/(n-k)!*a(n-k)*sumdiv(k, d, -d*d!^(-k/d)))))} [Hanna]

CROSSREFS

Cf. A005651, A007837.

Sequence in context: A329442 A281486 A047067 * A128849 A294495 A188289

Adjacent sequences:  A185892 A185893 A185894 * A185896 A185897 A185898

KEYWORD

sign

AUTHOR

Michael Somos, Feb 05 2011

STATUS

approved

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Last modified August 8 02:22 EDT 2020. Contains 336290 sequences. (Running on oeis4.)