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A014325 Four-fold convolution of Bell numbers with themselves. 5
1, 4, 14, 48, 169, 624, 2442, 10188, 45452, 217100, 1109914, 6064584, 35330715, 218788432, 1435302930, 9940062428, 72422364227, 553338786504, 4420324121772, 36820875272488, 319053830821880, 2869645346679368, 26739383194844404, 257682847299543248 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
G.f.: (1/(1 - x - x^2/(1 - 2*x - 2*x^2/(1 - 3*x - 3*x^2/(1 - 4*x - 4*x^2/(1 - ...))))))^4, a continued fraction. - Ilya Gutkovskiy, Sep 25 2017
G.f.: ( Sum_{j>=0} A000110(j)*x^j )^4. - G. C. Greubel, Jan 08 2023
MATHEMATICA
A014322[n_]:= Sum[BellB[j]*BellB[n-j], {j, 0, n}];
A014325[n_]:= Sum[A014322[j]*A014322[n-j], {j, 0, n}];
Table[A014325[n], {n, 0, 40}] (* G. C. Greubel, Jan 08 2023 *)
PROG
(Magma)
A014322:= func< n | (&+[Bell(j)*Bell(n-j): j in [0..n]]) >;
A014325:= func< n | (&+[A014322(j)*A014322(n-j): j in [0..n]]) >;
[A014325(n): n in [0..40]]; // G. C. Greubel, Jan 08 2023
(SageMath)
def A014322(n): return sum(bell_number(j)*bell_number(n-j) for j in range(n+1))
def A014325(n): return sum(A014322(j)*A014322(n-j) for j in range(n+1))
[A014325(n) for n in range(41)] # G. C. Greubel, Jan 08 2023
CROSSREFS
Column k=4 of A292870.
Sequence in context: A085280 A007851 A368555 * A047028 A220819 A047138
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified April 22 01:34 EDT 2024. Contains 371887 sequences. (Running on oeis4.)