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A365107
Sum_{n>=0} a(n) * x^n / n!^2 = exp( Sum_{n>=1} x^prime(n) / prime(n)!^2 ).
0
1, 0, 1, 1, 18, 101, 1550, 22492, 424536, 10283064, 272319552, 8959493401, 328044534576, 13799304374077, 657306569855728, 34694458662034731, 2048559070407831424, 132868259271772801185, 9463476338179250300352, 736376651361995115417850, 62178423492630241909006224, 5689134205956573233701281462
OFFSET
0,5
FORMULA
a(0) = 1; a(n) = (1/n) * Sum_{p <= n, p prime} binomial(n,p)^2 * p * a(n-p).
MATHEMATICA
nmax = 21; CoefficientList[Series[Exp[Sum[x^Prime[k]/Prime[k]!^2, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!^2
a[0] = 1; a[n_] := a[n] = (1/n) Sum[Binomial[n, Prime[k]]^2 Prime[k] a[n - Prime[k]], {k, 1, PrimePi[n]}]; Table[a[n], {n, 0, 21}]
CROSSREFS
Sequence in context: A140198 A107600 A229326 * A008528 A373316 A020881
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 21 2023
STATUS
approved