A205571
Expansion of e.g.f. 1/(1 - x*cosh(x)).
Original entry on oeis.org
1, 1, 2, 9, 48, 305, 2400, 22057, 230272, 2708001, 35412480, 509177801, 7986468864, 135718942801, 2483729876992, 48699677975145, 1018542257111040, 22634000289407297, 532557637644976128, 13226748101381102473, 345792863300174479360, 9492229607399841038961
Offset: 0
E.g.f.: A(x) = 1 + x + 2*x^2/2! + 9*x^3/3! + 48*x^4/4! + 305*x^5/5! +...
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CoefficientList[Series[1/(1-x*Cosh[x]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Feb 13 2013 *)
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{a(n)=n!*polcoeff(1/(1-x*cosh(x +x*O(x^n))),n)}
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a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = sum(k=0, n, k!*a185951(n, k)); \\ Seiichi Manyama, Feb 17 2025
A381209
Expansion of e.g.f. 1/(1 - x*cos(x))^3.
Original entry on oeis.org
1, 3, 12, 51, 216, 735, 0, -39081, -575232, -6047973, -48314880, -189159333, 3046957056, 99745485879, 1789140627456, 23433663134655, 185580069027840, -1250544374605389, -94781673979379712, -2543434372808424957, -47763303489939701760, -586864592847636893937
Offset: 0
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a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = sum(k=0, n, (k+2)!*I^(n-k)*a185951(n, k))/2;
A381206
Expansion of e.g.f. 1/(1 - x*cosh(x))^2.
Original entry on oeis.org
1, 2, 6, 30, 192, 1450, 12960, 133574, 1550976, 20055186, 285903360, 4452231982, 75186726912, 1368588922298, 26709799753728, 556339845854550, 12318065768693760, 288894650033594914, 7154212267816648704, 186545064693433665854, 5108590743587243950080
Offset: 0
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a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = sum(k=0, n, (k+1)!*a185951(n, k));
A381210
Expansion of e.g.f. 1/(1 - sinh(x))^3.
Original entry on oeis.org
1, 3, 12, 63, 408, 3123, 27552, 275103, 3065088, 37682883, 506606592, 7392091743, 116329479168, 1963781841843, 35395627487232, 678401549017983, 13776623985819648, 295481239628640003, 6674320861079273472, 158364407589097613823, 3937958237874411798528
Offset: 0
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a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a(n) = sum(k=0, n, (k+2)!*a136630(n, k))/2;
A381211
Expansion of e.g.f. 1/(1 - sin(x))^3.
Original entry on oeis.org
1, 3, 12, 57, 312, 1923, 13152, 98697, 805632, 7102563, 67233792, 679970937, 7315786752, 83421156003, 1004860895232, 12749105088777, 169926064668672, 2373678328434243, 34676591077097472, 528758667342524217, 8400613520498491392, 138830752520282729283
Offset: 0
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a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a(n) = sum(k=0, n, (k+2)!*I^(n-k)*a136630(n, k))/2;
Showing 1-5 of 5 results.
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