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A320329 Row sums of A174790. 1
1, 2, 7, 76, 1301, 26406, 619207, 16652168, 508596489, 17457431050, 666726681611, 28076838451212, 1293333060096013, 64713740778086414, 3495868307630899215, 202800355058036736016, 12574907509808996352017, 829987773918052958208018, 58100729276791270637568019 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..18.

FORMULA

a(n) = Sum_{m=0..n} 1 + ((-1 + binomial(n, m))*(n!)^2)/(m!*(-m + n)!).

a(n) = 1 + n - 2^n*n*(-1 + n)! + 4^n*Gamma(1/2 + n)/sqrt(Pi) for n > 0.

a(n) = 1 + A001477(n) - A000079(n)*A001477(n)*A000142(n - 1) + A000302(n)*Gamma(1/2 + A001477)/sqrt(Pi) for n > 0.

MAPLE

a := n -> add(1+((-1+binomial(n, m))*(n!)^2)/(m!*(-m+n)!), m = 0 .. n): seq(a(n), n = 0 .. 20);

MATHEMATICA

T[n_, m_] = 1+((-1+Binomial[n, m])(n!)^2)/(m!(-m + n)!); Table[Sum[T[n, m], {m, 0, n}], {n, 0, 20}] (* or *)

a[n_]:=1 + n - 2^n n (-1 + n)! + (4^n (Gamma[(1/2) + n]))/Sqrt[\[Pi]]; Join[{1}, Array[a, 20]]

PROG

(GAP) List([0..20], n->Sum([0..n], m->1 + ((- 1 + Binomial(n, m))*(Factorial(n)^2)/(Factorial(m)*Factorial(-m+n)))));

(PARI) a(n) = sum(m=0, n, 1 + ((- 1 + binomial(n, m))*(n!)^2)/(m!*(-m+n)!));

CROSSREFS

Row sums of A174790.

Cf. A001477, A000079, A000142, A000302.

Sequence in context: A064646 A144905 A266880 * A083455 A083829 A067963

Adjacent sequences:  A320326 A320327 A320328 * A320330 A320331 A320332

KEYWORD

nonn

AUTHOR

Stefano Spezia, Dec 18 2018

STATUS

approved

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Last modified April 1 02:10 EDT 2020. Contains 333153 sequences. (Running on oeis4.)