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A014347 Three-fold exponential convolution of primes with themselves. 5
8, 36, 168, 786, 3660, 16866, 76752, 343914, 1514724, 6543066, 27699960, 114793386, 466078116, 1854554490, 7248419496, 27869755866, 105687130980, 395978680266, 1468425404328, 5396913313866, 19675676962308, 71219609783946, 256052236665192, 914773982356902 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

E.g.f.: (Sum_{k>=0} prime(k+1)*x^k/k!)^3. - Ilya Gutkovskiy, Mar 10 2018

MAPLE

b:= proc(n, k) option remember; `if`(k=1,

      ithprime(n+1), add(b(j, floor(k/2))*

      b(n-j, ceil(k/2))*binomial(n, j), j=0..n))

    end:

a:= n-> b(n, 3):

seq(a(n), n=0..30);  # Alois P. Heinz, Mar 10 2018

MATHEMATICA

b[n_, k_] := b[n, k] = If[k == 1, Prime[n + 1], Sum[b[j, Floor[k/2]] b[n - j, Ceiling[k/2]] Binomial[n, j], {j, 0, n}]];

a[n_] := b[n, 3];

Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, Jun 05 2018, after Alois P. Heinz *)

CROSSREFS

Cf. A000040, A014345, A014352.

Sequence in context: A200250 A207099 A055064 * A200053 A164545 A199310

Adjacent sequences:  A014344 A014345 A014346 * A014348 A014349 A014350

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 19 09:33 EST 2020. Contains 332041 sequences. (Running on oeis4.)