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A343929 a(n) = Sum_{k=0..n} (k!)^(n+1) * binomial(n,k). 3
1, 2, 11, 1348, 7993925, 2986939982086, 100308280020162672007, 416336818263472141683094788104, 281633775231427434285800695714399092181001, 39594086714441777969538839399390619086007952991080833034 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..29

FORMULA

a(n) = [x^n] Sum_{k>=0} (k!)^(n+1) * x^k/(1 - x)^(k+1).

a(n) = n! * [x^n] exp(x) * Sum_{k>=0} (k!)^n * x^k.

MATHEMATICA

a[n_] := Sum[(k!)^(n+1) * Binomial[n, k], {k, 0, n} ]; Array[a, 10, 0] (* Amiram Eldar, May 04 2021 *)

PROG

(PARI) a(n) = sum(k=0, n, k!^(n+1)*binomial(n, k));

CROSSREFS

Cf. A046662, A343898, A343900, A343928.

Sequence in context: A131316 A062636 A343900 * A051254 A095820 A101295

Adjacent sequences:  A343926 A343927 A343928 * A343930 A343931 A343932

KEYWORD

nonn

AUTHOR

Seiichi Manyama, May 04 2021

STATUS

approved

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Last modified August 2 12:25 EDT 2021. Contains 346423 sequences. (Running on oeis4.)