A326983
Coefficients in asymptotic expansion of sequence A309618.
Original entry on oeis.org
1, 0, 2, 2, 10, 50, 250, 1442, 9514, 68882, 539098, 4546562, 41123338, 396400754, 4050377146, 43694283362, 495985850602, 5906224845266, 73578420729754, 956597103241922, 12951012525806026, 182233188537332018, 2660301596873941882, 40226477151229612322
Offset: 0
A309618(n) / n! ~ 1 + 2/n^2 + 2/n^3 + 10/n^4 + 50/n^5 + 250/n^6 + ...
A309619
a(n) = Sum_{k=0..floor(n/2)} k! * (n - 2*k)!.
Original entry on oeis.org
1, 1, 3, 7, 28, 128, 754, 5178, 41124, 368220, 3670872, 40290744, 482716896, 6267697920, 87664818960, 1313983544400, 21010949076960, 357007805477280, 6423473819220480, 122003441554176000, 2439346762501367040, 51213306647556506880, 1126446562222595147520
Offset: 0
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nmax = 25; CoefficientList[Series[Sum[k!*x^k, {k, 0, nmax}]*Sum[k!*x^(2*k), {k, 0, nmax}], {x, 0, nmax}], x]
Table[Sum[k!*(n-2*k)!, {k, 0, Floor[n/2]}], {n, 0, 25}]
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a(n) = sum(k=0, n\2, k! * (n - 2*k)!); \\ Michel Marcus, Dec 08 2020
Showing 1-2 of 2 results.