A379614 a(n) = Sum_{k=0..n} 2^((n + k - 1)*(n - k)/2) * n! / (n - k)!. Row sums of A365638.
1, 2, 8, 62, 920, 26104, 1420496, 148881328, 30184791424, 11884978702720, 9119462417850112, 13676896785924429056, 40193177909606893812736, 231954028321633491248270336, 2633539132301114752459257620480, 58919202504421532088999537276311552, 2601059501207939343360641860628003520512
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..81
Programs
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Magma
A379614:= func< n | (&+[Factorial(k)*Binomial(n,k)*2^(Binomial(n-k,2) +k*(n-k)): k in [0..n]]) >; [A379614(n): n in [0..20]]; // G. C. Greubel, Mar 19 2025
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Maple
a := n -> add(2^(((n + k - 1)*(n - k))/2) * n! / (n - k)!, k = 0..n): seq(a(n), n = 0..16);
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Mathematica
Table[Sum[2^(((n + k - 1)*(n - k))/2)*n!/(n - k)!, {k, 0, n} ], {n, 0, 16}] (* Michael De Vlieger, Dec 31 2024 *) -
SageMath
def A379614(n): return sum(factorial(k)*binomial(n,k)*2^(binomial(n-k,2) +k*(n-k)) for k in range(n+1)) print([A379614(n) for n in range(21)]) # G. C. Greubel, Mar 19 2025
Formula
a(n) ~ sqrt(Pi/log(2)) * 2^(n*(n-1)/2 + 5/8) * n^((1 + log(n)/log(2))/2). - Vaclav Kotesovec, Mar 19 2025
Comments