A330254
Expansion of e.g.f. Sum_{k>=1} sinh(x^k).
Original entry on oeis.org
1, 2, 7, 24, 121, 840, 5041, 40320, 423361, 3659040, 39916801, 558835200, 6227020801, 87195588480, 1536517382401, 20922789888000, 355687428096001, 7469453633241600, 121645100408832001, 2453176191578112000, 59616236292028416001
Offset: 1
-
nmax = 21; CoefficientList[Series[Sum[Sinh[x^k], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[n! DivisorSum[n, 1/#! &, OddQ[#] &], {n, 1, 21}]
A330504
Expansion of e.g.f. Sum_{k>=1} tanh(x^k).
Original entry on oeis.org
1, 2, 4, 24, 136, 480, 4768, 40320, 249856, 4112640, 39563008, 319334400, 6249389056, 82473431040, 1044235737088, 20922789888000, 355897293438976, 4408265775513600, 121616011523719168, 2757288942600192000, 31308290669925892096
Offset: 1
-
nmax = 21; CoefficientList[Series[Sum[Tanh[x^k], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
A155585[n_] := Sum[StirlingS2[n, k] (-2)^(n - k) k!, {k, 0, n}]; a[n_] := n! DivisorSum[n, A155585[#]/#! &]; Table[a[n], {n, 1, 21}]
Table[n! DivisorSum[n, 2^(# + 1) (2^(# + 1) - 1) BernoulliB[# + 1]/(# + 1)! &, OddQ[#] &], {n, 1, 21}]
A330528
Expansion of e.g.f. Sum_{k>=1} (sec(x^k) - 1) (even powers only).
Original entry on oeis.org
1, 17, 421, 29945, 1864921, 382577645, 43788506581, 15558403000145, 3746015060385841, 1757547389533786325, 562069712763196977901, 516878970296221633758905, 201649817635812110915892361, 216661054181289983631892988285
Offset: 1
-
nmax = 14; Table[(CoefficientList[Series[Sum[(Sec[x^k] - 1), {k, 1, nmax}], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}] // Rest
Table[(2 n)! DivisorSum[n, Abs[EulerE[2 #]]/(2 #)! &], {n, 1, 14}]
A331338
E.g.f.: Sum_{k>=1} (1 - sech(x^k)) (even powers only).
Original entry on oeis.org
1, 7, 421, 10375, 1864921, 177588115, 43788506581, 5364386887855, 3746015060385841, 743097477083711275, 562069712763196977901, 208700966175150043937095, 201649817635812110915892361, 89621739407126401163202051715, 158792595367325562826629059282821
Offset: 1
-
nmax = 15; Table[(CoefficientList[Series[Sum[1 - Sech[x^k], {k, 1, nmax}], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}] // Rest
Table[-(2 n)! DivisorSum[n, EulerE[2 #]/(2 #)! &], {n, 1, 15}]
Showing 1-4 of 4 results.