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A357721 a(n) = Sum_{k=0..floor(n/2)} (-n)^k * Stirling1(n,2*k). 2
1, 0, -2, 9, -28, 0, 1200, -16464, 167904, -1393200, 7429240, 43124400, -2404571904, 55590286752, -1027511503200, 16489054310400, -222885864448000, 1994839594780032, 14489184835474272, -1470395490046560000, 54581408106475622400, -1608207353670788640000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Pochhammer Symbol.
FORMULA
a(n) = n! * [x^n] cos( sqrt(n) * log(1+x) ).
a(n) = (-1)^n * ( (sqrt(n) * i)_n + (-sqrt(n) * i)_n )/2, where (x)_n is the Pochhammer symbol and i is the imaginary unit.
PROG
(PARI) a(n) = sum(k=0, n\2, (-n)^k*stirling(n, 2*k, 1));
(PARI) a(n) = round(n!*polcoef(cos(sqrt(n)*log(1+x+x*O(x^n))), n));
(PARI) a(n) = (-1)^n*round((prod(k=0, n-1, sqrt(n)*I+k)+prod(k=0, n-1, -sqrt(n)*I+k)))/2;
CROSSREFS
Main diagonal of A357720.
Sequence in context: A115186 A243560 A090900 * A155472 A100293 A202679
KEYWORD
sign
AUTHOR
Seiichi Manyama, Oct 10 2022
STATUS
approved

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Last modified April 18 11:00 EDT 2024. Contains 371779 sequences. (Running on oeis4.)