A353079 Exponential transform of odd primes.

1, 3, 14, 79, 521, 3876, 31935, 287225, 2791122, 29066589, 322292257, 3784650052, 46857941291, 609360372095, 8296220760974, 117914344818807, 1745211622467633, 26838798853062516, 428009369349905497, 7065576909286562195, 120545067517808693300, 2122393931891338237325, 38512344746420591905771

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

E.g.f.: exp( Sum_{k>=1} prime(k+1) * x^k / k! ).

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * prime(k+1) * a(n-k).

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*
      ithprime(j+1)*binomial(n-1, j-1), j=1..n))
    end:
seq(a(n), n=0..22);  # Alois P. Heinz, Apr 27 2022

Mathematica

nmax = 22; CoefficientList[Series[Exp[Sum[Prime[k + 1] x^k/k!, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] Prime[k + 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 22}]

Crossrefs

Cf. A007446, A065091, A300632.

Sequence in context: A086621 A020089 A218677 * A305128 A027614 A306040

Adjacent sequences: A353076 A353077 A353078 * A353080 A353081 A353082

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 22 2022

Status

approved