A014352 Four-fold exponential convolution of primes with themselves.

16, 96, 592, 3680, 22888, 141776, 872296, 5320160, 32116168, 191634736, 1128985544, 6560592320, 37577101096, 212032652336, 1178400630472, 6450745788064, 34795044655624, 185041871051312, 971039709861320, 5033044804735360, 25793494764933224, 130834363186542320

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!)^4. - 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, 4):
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, 4];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jun 05 2018, after Alois P. Heinz *)

Crossrefs

Cf. A000040, A014345, A014347.

Sequence in context: A321851 A185789 A322617 * A083295 A044267 A044648

Adjacent sequences: A014349 A014350 A014351 * A014353 A014354 A014355

Keyword

nonn

Author

N. J. A. Sloane

Status

approved