A217284
a(n) = Sum_{k=0..n} (n!/k!)^3.
Original entry on oeis.org
1, 2, 17, 460, 29441, 3680126, 794907217, 272653175432, 139598425821185, 101767252423643866, 101767252423643866001, 135452212975869985647332, 234061424022303335198589697, 514232948577000427431301564310, 1411055210895289172871491492466641, 4762311336771600958441283787074913376
Offset: 0
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Table[Sum[(n!/k!)^3, {k, 0, n}], {n, 0, 20}]
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a(n) = sum(k=0, n, (n!/k!)^3); \\ Seiichi Manyama, May 02 2021
A343928
a(n) = Sum_{k=0..n} (k!)^n * binomial(n,k).
Original entry on oeis.org
1, 2, 7, 244, 337061, 24923091206, 139331988275478727, 82607113404338664216300296, 6984967577834038055008791270166057993, 109110690950275218023122492287310115968068596613130, 395940866518366059877297056617763923418318903997411043997258716171
Offset: 0
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a[n_] := Sum[(k!)^n * Binomial[n, k], {k, 0, n} ]; Array[a, 11, 0] (* Amiram Eldar, May 04 2021 *)
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a(n) = sum(k=0, n, k!^n*binomial(n, k));
A343863
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = (n!)^k * Sum_{j=1..n} (1/j!)^k.
Original entry on oeis.org
1, 1, 2, 1, 2, 3, 1, 2, 5, 4, 1, 2, 9, 16, 5, 1, 2, 17, 82, 65, 6, 1, 2, 33, 460, 1313, 326, 7, 1, 2, 65, 2674, 29441, 32826, 1957, 8, 1, 2, 129, 15796, 684545, 3680126, 1181737, 13700, 9, 1, 2, 257, 94042, 16175105, 427840626, 794907217, 57905114, 109601, 10
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, ...
2, 2, 2, 2, 2, 2, ...
3, 5, 9, 17, 33, 65, ...
4, 16, 82, 460, 2674, 15796, ...
5, 65, 1313, 29441, 684545, 16175105, ...
6, 326, 32826, 3680126, 427840626, 50547203126, ...
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T[n_, k_] := Sum[(n!/j!)^k, {j, 0, n}]; Table[T[k, n - k], {n, 0, 9}, {k, 0, n}] // Flatten (* Amiram Eldar, May 03 2021 *)
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T(n, k) = sum(j=0, n, (n!/j!)^k);
A336248
a(n) = (n!)^n * Sum_{k=0..n} (-1)^k / (k!)^n.
Original entry on oeis.org
1, 0, 1, 26, 20481, 774403124, 2173797080953345, 645067515585218711490294, 27280857986486289638369834192338945, 213095986405176211170558965907644717041658073416, 386654453940903446694477049963665295677203885863801760000000001
Offset: 0
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Table[(n!)^n Sum[(-1)^k/(k!)^n, {k, 0, n}], {n, 0, 10}]
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a(n) = (n!)^n * sum(k=0, n, (-1)^k / (k!)^n); \\ Michel Marcus, Jul 14 2020
Showing 1-4 of 4 results.