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A295610
a(n) = Sum_{k=0..n} (n!/(n - k)!)^k.
1
1, 2, 7, 256, 345749, 25090776406, 139507578065088907, 82622801516492599819822772, 6985137485409222182920705065038896201, 109110989095384931538566720095053550173384985449034, 395940975233113726268241745444050219538058574725338743701918216111
OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Binomial Sums
FORMULA
a(n) = Sum_{k=0..n} A219206(n,k)*A036740(k).
a(n) ~ 2^(n/2) * Pi^(n/2) * n^(n^2 + n/2) / exp(n^2 - 1/12). - Vaclav Kotesovec, Nov 25 2017
MATHEMATICA
Table[Sum[(n!/(n - k)!)^k, {k, 0, n}], {n, 0, 10}]
Table[Sum[(Gamma[n + 1]/Gamma[k + 1])^(n - k), {k, 0, n}], {n, 0, 10}]
Table[Sum[(Binomial[n, k] k!)^k, {k, 0, n}], {n, 0, 10}]
PROG
(PARI) a(n) = sum(k=0, n, (n!/(n - k)!)^k); \\ Michel Marcus, Nov 25 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 24 2017
STATUS
approved