A381382
E.g.f. A(x) satisfies A(x) = 1/( 1 - sinh(x * A(x)^2) / A(x)^2 ).
Original entry on oeis.org
1, 1, 2, 7, 48, 541, 7600, 120891, 2178176, 45053401, 1065957888, 28344376303, 831973593088, 26647344263541, 925300511922176, 34668496386129763, 1394928344160731136, 59986286728056665905, 2744940504174063714304, 133158543838350039763671
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!*binomial(2*n-k+1, k)/(2*n-k+1)*a136630(n, k));
A381384
E.g.f. A(x) satisfies A(x) = 1/( 1 - sin(x * A(x)^2) / A(x)^2 ).
Original entry on oeis.org
1, 1, 2, 5, 0, -299, -5840, -90791, -1210496, -11174519, 71397888, 8367496301, 327020705792, 9709296136541, 226223975684096, 2946493117173761, -87437164233621504, -9675847870039338095, -535455805780063748096, -22518479178045130002731, -706013052362778282033152
Offset: 0
-
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!*binomial(2*n-k+1, k)/(2*n-k+1)*I^(n-k)*a136630(n, k));
A381409
E.g.f. A(x) satisfies A(x) = exp( x * cos(x * A(x)^2) ).
Original entry on oeis.org
1, 1, 1, -2, -59, -744, -6419, -6096, 1504553, 47199232, 911415481, 7309642880, -338340409043, -21607316073472, -725479564376475, -13094500078091264, 245361657851526353, 35579148236923486208, 1875350389057457406193, 57582879572195726819328
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, (2*n-2*k+1)^(k-1)*I^(n-k)*a185951(n, k));
A381520
Expansion of e.g.f. ( (1/x) * Series_Reversion( x/(1 + x * cos(x))^2 ) )^(1/2).
Original entry on oeis.org
1, 1, 4, 27, 240, 2345, 17280, -226597, -21007616, -1007159823, -42976972800, -1775328986981, -72123329507328, -2843431148886887, -103621659777126400, -2971936506262036965, -6719764584265482240, 9528526268302653725537, 1192610999728818101551104
Offset: 0
-
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!*binomial(2*n+1, k)*I^(n-k)*a185951(n, k))/(2*n+1);
A381379
E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cos(x * A(x)) )^2.
Original entry on oeis.org
1, 2, 6, 18, -48, -2630, -52800, -824054, -8682240, 54462258, 7410631680, 305163480578, 8935815871488, 167137193150954, -1440976761090048, -349400091225243270, -22113174143289262080, -960586728800597050526, -26252145855684866211840, 255024367557922004307442
Offset: 0
-
a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = 2*sum(k=0, n, k!*binomial(2*n-k+2, k)/(2*n-k+2)*I^(n-k)*a185951(n, k));
Showing 1-5 of 5 results.
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