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A357683 a(n) = Sum_{k=0..floor(n/2)} n^k * |Stirling1(n,2*k)|. 4
1, 0, 2, 9, 60, 500, 4920, 55566, 706720, 9979200, 154706760, 2609691700, 47547916416, 929943488448, 19421810408000, 431196538865400, 10137091700736000, 251485260368396288, 6563768030597826720, 179746132716715050000, 5152012082327932518400 (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] cosh( sqrt(n) * log(1-x) ).
a(n) = ( (sqrt(n))_n + (-sqrt(n))_n )/2, where (x)_n is the Pochhammer symbol.
a(n) ~ n^(n + sqrt(n)/2 - 1/4) / (2*exp(n - sqrt(n) - 1/2)) * (1 - 3/(4*sqrt(n))). - Vaclav Kotesovec, Oct 10 2022
PROG
(PARI) a(n) = sum(k=0, n\2, n^k*abs(stirling(n, 2*k, 1)));
(PARI) a(n) = round(n!*polcoef(cosh(sqrt(n)*log(1-x+x*O(x^n))), n));
(PARI) a(n) = round((prod(k=0, n-1, sqrt(n)+k)+prod(k=0, n-1, -sqrt(n)+k)))/2;
CROSSREFS
Sequence in context: A116364 A354314 A354496 * A120970 A339360 A111558
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 09 2022
STATUS
approved

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Last modified May 21 05:34 EDT 2024. Contains 372728 sequences. (Running on oeis4.)