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A300631 a(n) = n! * [x^n] (Sum_{k=0..n} prime(k+1)*x^k/k!)^n. 1
1, 3, 38, 786, 22888, 857800, 39316464, 2130380560, 133222474368, 9443111340672, 748168002970880, 65520799156209408, 6284786657494483968, 655287035001111884800, 73792143714173551392768, 8925528145554323771934720, 1154065253662722209679572992, 158849709577131169400652988416 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..333

N. J. A. Sloane, Transforms

EXAMPLE

The table of coefficients of x^k in expansion of e.g.f. (Sum_{k>=0} prime(k+1)*x^k/k!)^n begins:

n = 0:  (1),   0,     0,      0,       0,        0,  ... (A000007)

n = 1:   2,   (3),    5,      7,      11,       13,  ... (A000040, with offset 0)

n = 2:   4,   12,   (38),   118,     362,     1082,  ... (A014345)

n = 3:   8,   36,   168,   (786),   3660,    16866,  ... (A014347)

n = 4:  16,   96,   592,   3680,  (22888),  141776,  ... (A014352)

n = 5:  32,  240,  1840,  14240,  110560,  (857800), ...

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-> `if`(n=0, 1, b(n$2)):

seq(a(n), n=0..20);  # Alois P. Heinz, Mar 10 2018

MATHEMATICA

Table[n! SeriesCoefficient[Sum[Prime[k + 1] x^k/k!, {k, 0, n}]^n, {x, 0, n}], {n, 0, 17}]

CROSSREFS

Cf. A000007, A000040, A014345, A014347, A014352.

Sequence in context: A228697 A072331 A109518 * A300627 A158119 A263332

Adjacent sequences:  A300628 A300629 A300630 * A300632 A300633 A300634

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 10 2018

STATUS

approved

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Last modified September 22 13:36 EDT 2020. Contains 337289 sequences. (Running on oeis4.)