A330605
a(n) = exp(-1) * Sum_{k>=0} (n*k - 1)^n / k!.
Original entry on oeis.org
1, 0, 5, 89, 2737, 121399, 7316101, 572218716, 56142822849, 6731180810945, 965898950508901, 163116461798211503, 31969444766902475185, 7187057932197297484108, 1834860441330563739401765, 527403671798720265634312349, 169396494914472404237224898305
Offset: 0
-
Table[Exp[-1] Sum[(n k - 1)^n/k!, {k, 0, Infinity}], {n, 0, 16}]
Join[{1}, Table[Sum[(-1)^(n - k) Binomial[n, k] n^k BellB[k], {k, 0, n}], {n, 1, 16}]]
Table[n! SeriesCoefficient[Exp[Exp[n x] - x - 1], {x, 0, n}], {n, 0, 16}]
A307080
a(n) = exp(1) * Sum_{k>=0} (-1)^k*(n*k + 1)^n/k!.
Original entry on oeis.org
1, 0, -3, 19, 497, -1899, -489491, -15433676, 618450881, 120846851155, 7012261819901, -467816186167659, -175527285590430863, -20961845760818684812, 568194037748383908653, 898095630359015975379151, 220433074470274983356464897, 16144974747716546214909454181
Offset: 0
-
Table[Exp[1] Sum[(-1)^k (n k + 1)^n/k!, {k, 0, Infinity}], {n, 0, 17}]
Table[n! SeriesCoefficient[Exp[1 + x - Exp[n x]], {x, 0, n}], {n, 0, 17}]
Join[{1}, Table[Sum[Binomial[n, k] n^k BellB[k, -1], {k, 0, n}], {n, 1, 17}]]
A308864
a(n) = Sum_{k>=0} (n*k + 1)^n/2^(k+1).
Original entry on oeis.org
1, 2, 17, 442, 22833, 1942026, 245246761, 43001877122, 9986424563009, 2965574161158490, 1095862246322273601, 493067173454342315346, 265360795458419332828657, 168311426029488910748596394, 124248479512164840358578103577, 105608722927065949313865618984226
Offset: 0
-
Table[Sum[(n k + 1)^n/2^(k + 1), {k, 0, Infinity}], {n, 0, 15}]
Table[n! SeriesCoefficient[Exp[x]/(2 - Exp[n x]), {x, 0, n}], {n, 0, 15}]
Join[{1}, Table[Sum[Binomial[n, k] n^k HurwitzLerchPhi[1/2, -k, 0]/2, {k, 0, n}], {n, 1, 15}]]
A367784
a(n) = exp(1) * Sum_{k>=0} (-1)^k * (n*k - 1)^n / k!.
Original entry on oeis.org
1, -2, 5, 17, 17, -8151, -311435, -777974, 927723585, 82906687673, 1693962380101, -707005824990631, -137258747025993071, -10253960705018807830, 1697644859939460151413, 803696888217607331079149, 148126297324647875348070657, -323461353221296480463456191
Offset: 0
-
Table[n! SeriesCoefficient[Exp[1 - x - Exp[n x]], {x, 0, n}], {n, 0, 17}]
Unprotect[Power]; 0^0 = 1; Table[Sum[(-1)^(n - k) Binomial[n, k] n^k BellB[k, -1], {k, 0, n}], {n, 0, 17}]
Showing 1-4 of 4 results.